Relevant bibliographies by topics / Integrability

Academic literature on the topic 'Integrability'

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Published: 4 June 2021
Last updated: 7 July 2024

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Journal articles on the topic "Integrability"

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Jarník, Jiří, and Jaroslav Kurzweil. "Pfeffer integrability does not imply $M_1$-integrability." Czechoslovak Mathematical Journal 44, no. 1 (1994): 47–56. http://dx.doi.org/10.21136/cmj.1994.128454.

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Schurle, Arlo W. "Perron Integrability Versus Lebesgue Integrability." Canadian Mathematical Bulletin 28, no. 4 (December 1, 1985): 463–68. http://dx.doi.org/10.4153/cmb-1985-055-1.

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AbstractThe paper investigates the relationship between Perron - Stieltjes integrability and Lebesgue-Stieltjes integrability within the generalized Riemann approach. The main result states that with certain restrictions a Perron-Stieltjes integrable function is locally Lebesgue-Stieltjes integrable on an open dense set. This is then applied to show that a nonnegative Perron-Stieltjes integrable function is Lebesgue-Stieltjes integrable. Finally, measure theory is invoked to remove the restrictions in the main result.
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Mussardo, G. "Integrability, non-integrability and confinement." Journal of Statistical Mechanics: Theory and Experiment 2011, no. 01 (January 6, 2011): P01002. http://dx.doi.org/10.1088/1742-5468/2011/01/p01002.

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Kozak, A. V. "Integrability in AdS/CFT." Ukrainian Journal of Physics 58, no. 11 (November 2013): 1108–12. http://dx.doi.org/10.15407/ujpe58.11.1108.

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KUŚ, MAREK. "Integrability and non-integrability in quantum mechanics." Journal of Modern Optics 49, no. 12 (October 2002): 1979–85. http://dx.doi.org/10.1080/09500340210140759.

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Khesin, Boris, and Fedor Soloviev. "Non-integrability vs. integrability in pentagram maps." Journal of Geometry and Physics 87 (January 2015): 275–85. http://dx.doi.org/10.1016/j.geomphys.2014.07.027.

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M. Saadoune and R. Sayyad. "From Scalar McShane Integrability to Pettis Integrability." Real Analysis Exchange 38, no. 2 (2013): 445. http://dx.doi.org/10.14321/realanalexch.38.2.0445.

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Ünsal, Ömer, and Filiz Taşcan. "Soliton Solutions, Bäcklund Transformation and Lax Pair for Coupled Burgers System via Bell Polynomials." Zeitschrift für Naturforschung A 70, no. 5 (May 1, 2015): 359–63. http://dx.doi.org/10.1515/zna-2015-0076.

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AbstractIn this work, we apply the binary Bell polynomial approach to coupled Burgers system. In other words, we investigate possible integrability of referred system. Bilinear form and soliton solutions are obtained, some figures related to these solutions are given. We also get Bäcklund transformations in both binary Bell polynomial form and bilinear form. Based on the Bäcklund transformation, Lax pair is obtained. Namely, this is a study in which integrabilitiy of coupled burgers system is investigated.
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Stefansson, Gunnar F. "Pettis Integrability." Transactions of the American Mathematical Society 330, no. 1 (March 1992): 401. http://dx.doi.org/10.2307/2154171.

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GAETA, GIUSEPPE. "QUATERNIONIC INTEGRABILITY." Journal of Nonlinear Mathematical Physics 18, no. 3 (January 2011): 461–74. http://dx.doi.org/10.1142/s1402925111001714.

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Dissertations / Theses on the topic "Integrability"

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Clarke, Daniel. "Integrability in submanifold geometry." Thesis, University of Bath, 2012. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.558890.

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This thesis concerns the relationship of submanifold geometry, in both the smooth and discrete sense, to representation theory and the theory of integrable systems. We obtain Lie theoretic generalisations of the transformation theory of projectively and Lie applicable surfaces, and M�obius-flat submanifolds of the conformal n-sphere. In the former case, we propose a discretisation. We develop a projective approach to centro-ane hypersurfaces, analogous to the conformal approach to submanifolds in spaceforms. This yields a characterisation of centro-ane hypersurfaces amongst M�obius-flat projective hypersurfaces using polynomial conserved quantities. We also propose a discretisation of curved flats in symmetric spaces. After developing the transformation theory for this, we see how Darboux pairs of discrete isothermicnets arise as discrete curved flats in the symmetric space of opposite point pairs. We show how discrete curves in the 2-sphere fit into this framework.
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Young, Charles Alastair Stephen. "Integrability and symmetric spaces." Thesis, University of Cambridge, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.614914.

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Coletta, Meredith L. Hicks R. Andrew. "Integrability in optical design /." Philadelphia, Pa. : Drexel University, 2009. http://hdl.handle.net/1860/3079.

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Engbrant, Fredrik. "Supersymmetric Quantum Mechanics and Integrability." Thesis, Uppsala universitet, Teoretisk fysik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-173301.

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This master’s thesis investigates the relationship between supersymmetry and integrability in quantum mechanics. This is done by finding a suitable way to systematically add more supersymmetry to the system. Adding more super- symmetry will give constraints on the potential which will lead to an integrable system. A possible way to explore the integrability of supersymmetric quantum mechanics was introduced in a paper by Crombrugghe and Rittenberg in 1983, their method has been used as well as another approach based on expanding a N = 1 system by introducing complex structures. N = 3 or more supersymmetry is shown to give an integrable system.
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Scott, Daniel R. D. "Separation of variables and integrability." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.389963.

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Chen, Y.-C. "Anti-integrability in Lagrangian systems." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.597512.

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Three examples of application of the anti-integrability concept in Lagrangian systems are proved, concerning the continuation of a class of trajectories from the anti-integrable limit. All three examples were proposed by Robert S. MacKay. The first example arises in adiabatically perturbed systems. With an assumption that the adiabatic Poincaré-Melnikov function has simple zeros, we constructed a variational functional whose critical points give rise to a sequence of homoclinic trajectories for the unperturbed Lagrangian in the adiabatic limit but a sequence of multi-bump trajectories under perturbations. We found there is a compact set, which is a Cantor set, such that the Poincaré map induced by the phase flow restricting to it is conjugate to the Bernoulli shift, in our case, with three symbols. Hence the approach of the anti-integrability to the adiabatically perturbed problems is equivalent to the one which combines the Poincaré-Melnikov method and the Birkhoff-Smale theory. The second example occurs in the Sinai billiard system. The anti-integrable limit is the limit when the radius of the scatterer-disc goes down to zero, and the system becomes "δ-billiards". The orbits of the δ-billiards are the anti-integrable orbits which are piecewise straight lines joining zero-radius discs to discs, and are easily obtained. Under some non-degeneracy conditions, we proved all anti-integrable orbits can be continued to the small radius case, and found that any periodic orbit has infinitely many homoclinic orbits as well as heteroclinic orbits to any others. These exists a compact set, which is also a Cantor set, such that the billiard map restricted to it is conjugate to a subshift of finite type with an arbitrarily given number of symbols. We studied in the third example when the scatterers are approximated by repulsive potentials such as the Coulomb potential ε/r, where ε and r are non-negative numbers and r is the distance from the potential centre. In the Coulomb potential case, the anti-integrable limit is the ε → 0, and the system becomes the δ-billiard system. Then we found that the results in the Sinai billiards also hold here when ε > 0 but small. More general type of repulsive potentials were also investigated and a sufficient condition under which anti-integrable trajectories persist was given.
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Zhao, Peng. "Integrability in supersymmetric gauge theories." Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.648125.

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Katsimpouri, Despoina. "Integrability in two-dimensional gravity." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://dx.doi.org/10.18452/17316.

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In dieser Arbeit untersuchen wir Gravitations- und Supergravitationssysteme, die in zwei Dimensionen vollständig integrabel sind. Dies sind Theorien, zu denen auch die einsteinsche Gravitation zählt, die bei dimensionaler Reduktion auf drei Dimensionen, die Form eines nichtlinearen $\s$-Models für den Materieteil annehmen und als Zielmannigfaltigkeit den Cosetraum $\mathrm{G}/\mathrm{K}$ haben. Ausgehend von der einsteinschen Gravitation betrachten wir insbesondere die Klasse der stationären und axialsymmetrischen Lösungen. Dabei untersuchen wir das lineare System (Lax-Paar), das den nichtlinearen Feldgleichungen der Vakuumsgravitation entspricht, wie es von Belinski-Zakharov (BZ) und Breitenlohner-Maison (BM) formuliert wurde. Die Existenz des linearen Systems zeigt die Integrabilität des zweidimensionalen Systems und ist inversen Streumethoden zugänglich, wie in zwei unterschiedlichen Ansätzen von BZ und BM gezeigt. Aus der unendlich-dimensionalen Symmetrie, die mit den zweidimensionalen Gleichungen assoziiert ist, ergibt sich die sogenannte Gerochgruppe. Der BM-Ansatz ermöglicht eine direkte Implementierung der Gerochgruppe und der Erzeugung von physikalisch interessanten Lösungen im Solitonensektor auf manifest gruppentheoretischer Weise. Aus diesem Grund ist zu erwarten, dass es in einem breiteren Spektrum von Cosetmodellen angewendet werden kann. In dieser Arbeit konzentrieren wir uns auf diesen Ansatz und erweitern ihn um die STU-Supergravitation, wobei entsprechende technische Änderungen im BM-Lösungserzeugungsalgorithmus erforderlich werden. Basierend auf diesen Änderungen, diskutieren wir auch eine Verallgemeinerung auf andere Fälle. Wir testen die Anwendbarkeit der BM inversen Streumethode, indem wir explizit folgende Lösungen konstruieren: die Kerr-NUT Lösung der einsteinschen Gravitation, die Vier-Ladungs-Lösung eines schwarzen Lochs innerhalb der STU Supergravitation von Cvetic und Youm und die einfach rotierende JMaRT Lösung.
In this thesis, we study gravity and supergravity systems that become completely integrable in two dimensions. Including Einstein gravity, these systems are theories that upon dimensional reduction to three dimensions assume the form of a non-linear $\s$-model for the matter part, with target manifold a coset space $\mathrm{G}/\mathrm{K}$. Starting from Einstein gravity and focusing on the class of stationary axisymmetric solutions, we study the linear system (Lax pair) associated with the non-linear field equations of vacuum gravity as formulated by Belinski - Zakharov (BZ) and Breitenlohner-Maison (BM). The existence of the linear system exhibits the integrability of the two-dimensional system and is amenable to inverse scattering methods as shown in two different approaches by BZ and BM. The infinite dimensional symmetry associated with the two-dimensional equations gives rise to the so-called Geroch group. The BM approach allows for a direct implementation of the Geroch group and the generation of physically interesting solutions in the soliton sector in a manifestly group theoretic way. For this reason, it is expected to apply to a broader set of coset models. Throughout this work, we concentrate on this approach and extend it to STU supergravity, where appropriate technical modifications were required in the BM solution generation algorithm. Based on these modifications, we also discuss a generalization to other set-ups. We test the applicability of the BM inverse scattering method by explicitly constructing the Kerr-NUT solution of Einstein gravity and within STU supergravity, the four-charge black hole solution of Cvetic and Youm as well as the singly rotating JMaRT solution.
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Gahramanov, Ilmar. "Superconformal indices, dualities and integrability." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17568.

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In dieser Arbeit behandeln wir exakte, nicht-perturbative Ergebnisse, die mithilfe der superkonformen Index-Technik, in supersymmetrischen Eichtheorien mit vier Superladungen (d. h. N=1 Supersymmetrie in vier Dimensionen und N=2 in drei Dimensionen) gewonnen wurden. Wir benutzen die superkonforme Index-Technik um mehrere Dualitäts Vermutungen in supersymmetrischen Eichtheorien zu testen. Wir führen Tests der dreidimensionalen Spiegelsymmetrie und Seiberg ähnlicher Dualitäten durch. Das Ziel dieser Promotionsarbeit ist es moderne Fortschritte in nicht-perturbativen supersymmetrischen Eichtheorien und ihre Beziehung zu mathematischer Physik darzustellen. Im Speziellen diskutieren wir einige interessante Identitäten der Integrale, denen einfache und hypergeometrische Funktionen genügen und ihren Bezug zu supersymmetrischen Dualitäten in drei und vier Dimensionen. Methoden der exakten Berechnungen in supersymmertischen Eichtheorien sind auch auf integrierbare statistische Modelle anwendbar. Dies wird im letzten Kapitel der vorliegenden Arbeit behandelt.
In this thesis we discuss exact, non-perturbative results achieved using superconformal index technique in supersymmetric gauge theories with four supercharges (which is N = 1 supersymmetry in four dimensions and N = 2 supersymmetry in three). We use the superconformal index technique to test several duality conjectures for supersymmetric gauge theories. We perform tests of three-dimensional mirror symmetry and Seiberg-like dualities. The purpose of this thesis is to present recent progress in non-perturbative supersymmetric gauge theories in relation to mathematical physics. In particular, we discuss some interesting integral identities satisfied by basic and elliptic hypergeometric functions and their relation to supersymmetric dualities in three and four dimensions. Methods of exact computations in supersymmetric theories are also applicable to integrable statistical models, which we discuss in the last chapter of the thesis.
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Debernardi, Pinos Alberto. "Convergence and integrability of fourier transforms." Doctoral thesis, Universitat Autònoma de Barcelona, 2018. http://hdl.handle.net/10803/463030.

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El propòsit d'aquesta tesi és el d'estudiar dos tipus de problema diferents per a certes transformades de Fourier. Primer investiguem la convergència uniforme d'integrals sinusoidals en una i dos dimensions. Per a dur a terme aquesta investigació, utilitzem una condicio de monotonia general, recentment introduïda, tot desenvolupant aquesta teoria en concordança amb les nostres necessitats. Com a resultats principals, obtenim condicions necessàries i suficients que les funcions monòtones generals han de satisfer per tal de poder assegurar la convergència uniforme de les seves respectives transformades sinusoidals (en una i dues dimensions). En segon lloc, estudiem la convergència puntual i uniforme de les transformades de Hankel amb pesos, a través de l'estudi de les condicions variacionals, d'integració i de magnitud de les funcions involucrades, amb especial èmfasi en les condicions variacionals. També utilitzem l'esmentada condició de monotonia general, que ens permet traduir condicions variacionals de les funcions en condicions d'integrabilitat o magnitud de les mateixes. Donem condicions suficients per a la convergència puntual, mentre que per a la convergència uniforme, també en donem de necessàries, quan és possible. En els casos en els quals només podem donar condicions suficients per a la convergència uniforme, també comentem l'optimalitat d'aquestes. Finalment, considerem transformades de Fourier generalitzades, i estudiem condicions necessàries i suficients per tal de garantir desigualtats de normes amb pesos entre funcions i les seves transformades. Les desigualtats de normes amb pesos es poden considerar com a versions quantitatives del principi d'incertesa. Donem especial rellevància a les desigualtats amb pesos del tipus funció potencial i les transformades sinusoidals, cosinusoidals, de Hankel, i de Struve. També utilitzem la condició de monotonia general en aquest problema, que ens permet obtenir condicions necessàries i suficients menys restrictives per poder garantir desigualtats de normes amb pesos.
The purpose of this dissertation is to study two different kind of problems for certain types of Fourier transforms. First, we investigate the uniform convergence of one and two-dimensional sine transforms. To this end, we make use of a general monotonicity condition that has been recently introduced, and develop the theory further according to our needs. We mainly obtain necessary and sufficient conditions on general monotone functions for the uniform convergence of their respective (single and double) sine integrals. Secondly, we study pointwise and uniform convergence of weighted Hankel transforms through an approach that consists on studying the variational, integrability, and magnitude conditions of the involved functions, with special emphasis on variational conditions. Here we also use the aforementioned general monotonicity, which allows us to translate from variational conditions to magnitude/integrability conditions of the functions. For the pointwise convergence only sufficient conditions are obtained, whilst for the uniform convergence, it is sometimes possible to obtain necessary and sufficient conditions. In the case when only sufficient conditions for the uniform convergence are given, the sharpness of those are discussed. 
Finally, we consider generalized Fourier transforms and study necessary and sufficient conditions for weighted norm inequalities between functions and their transforms to hold. Weighted norm inequalities can be considered as quantitative uncertainty principle relations. We particularly focus on inequalities with power weights and the sine, cosine, Hankel, and Struve transforms. We also make use of the general monotonicity condition in this problem, which allows us to obtain less restrictive necessary and sufficient for the weighted norm inequalities to hold.
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Books on the topic "Integrability"

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Mikhailov, Alexander V., ed. Integrability. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-88111-7.

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1953-, Mikhailov Alexander V., ed. Integrability. Berlin: Springer, 2009.

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1953-, Mikhailov Alexander V., ed. Integrability. Berlin: Springer, 2009.

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Zakharov, Vladimir E., ed. What Is Integrability? Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-88703-1.

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J, Mason L., and Nutku Yavuz, eds. Geometry and integrability. Cambridge, U.K: Cambridge University Press, 2003.

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Evgenévich, Zakharov Vladimir, and Calogero F, eds. What is integrability? Berlin: Springer-Verlag, 1991.

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F, Calogero, and Zakharov Vladimir Evgenʹevich, eds. What is integrability? Berlin: Springer-Verlag, 1990.

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Zakharov, Vladimir E. What Is Integrability? Berlin, Heidelberg: Springer Berlin Heidelberg, 1991.

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1941-, Kosmann-Schwarzbach Yvette, Grammaticos B. 1946-, and Tamizhmani K. M. 1954-, eds. Integrability of nonlinear systems. Berlin: Springer, 2004.

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Kosmann-Schwarzbach, Y., B. Grammaticos, and K. M. Tamizhmani, eds. Integrability of Nonlinear Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0113690.

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Book chapters on the topic "Integrability"

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Rudolph, Gerd, and Matthias Schmidt. "Integrability." In Theoretical and Mathematical Physics, 569–640. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-5345-7_11.

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Flaschka, H., A. C. Newell, and M. Tabor. "Integrability." In What Is Integrability?, 73–114. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-88703-1_3.

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Newton, Isaac. "Integrability." In Abstract Calculus, 327–44. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003166559-10.

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Arutyunov, Gleb. "Liouville Integrability." In Elements of Classical and Quantum Integrable Systems, 1–68. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-24198-8_1.

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Rădulescu, Teodora-Liliana T., Vicenţiu D. Rădulescu, and Titu Andreescu. "Riemann Integrability." In Problems in Real Analysis, 325–72. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-77379-7_9.

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Reichl, L. E. "Quantum Integrability." In The Transition to Chaos, 222–47. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4757-4352-4_5.

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Bartle, Robert. "Absolute integrability." In Graduate Studies in Mathematics, 101–13. Providence, Rhode Island: American Mathematical Society, 2001. http://dx.doi.org/10.1090/gsm/032/07.

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Steinmann, Paul. "Integrability and Non-Integrability in a Nutshell." In Geometrical Foundations of Continuum Mechanics, 493–99. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-46460-1_9.

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Bloch, A. M., and T. S. Ratiu. "Convexity and Integrability." In Symplectic Geometry and Mathematical Physics, 48–79. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4757-2140-9_3.

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Prüss, Jan. "Integrability of Resolvents." In Monographs in Mathematics, 256–83. Basel: Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-8570-6_10.

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Conference papers on the topic "Integrability"

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ANDERSON, I. M., M. E. FELS, and P. J. VASSILIOU. "ON DARBOUX INTEGRABILITY." In Proceedings of the International Conference on SPT 2007. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812776174_0002.

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Popowicz, Ziemowit, Wen Xiu Ma, Xing-biao Hu, and Qingping Liu. "Does the supersymmetric integrability imply the integrability of Bosonic sector." In NONLINEAR AND MODERN MATHEMATICAL PHYSICS: Proceedings of the First International Workshop. AIP, 2010. http://dx.doi.org/10.1063/1.3367239.

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Lulek, T. "Bethe Ansatz and Integrability." In Symmetry and Structural Properties of Condensed Matter. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813234345_0003.

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Mukanov, Zhalgas, and Dauren Matin. "Integrability of cosine transforms." In ADVANCEMENTS IN MATHEMATICAL SCIENCES: Proceedings of the International Conference on Advancements in Mathematical Sciences. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4930496.

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CARROLL, R. "STAR PRODUCTS AND INTEGRABILITY." In Proceedings of the 3rd ISAAC Congress. World Scientific Publishing Company, 2003. http://dx.doi.org/10.1142/9789812794253_0098.

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Fan and Wolff. "Surface curvature from integrability." In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. IEEE Comput. Soc. Press, 1994. http://dx.doi.org/10.1109/cvpr.1994.323876.

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Lamers, Jules. "Introduction to quantum integrability." In 10th Modave Summer School in Mathematical Physics. Trieste, Italy: Sissa Medialab, 2015. http://dx.doi.org/10.22323/1.232.0001.

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Tulczyjew, W. "The theory of systems with internal degrees of freedom." In Classical and Quantum Integrability. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc59-0-1.

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de León, M., J. C. Marrero, and D. Martín de Diego. "A new geometric setting for classical field theories." In Classical and Quantum Integrability. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc59-0-10.

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Libermann, Paulette. "Cartan connections and momentum maps." In Classical and Quantum Integrability. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc59-0-11.

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Reports on the topic "Integrability"

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Fally, Thibault. Integrability and Generalized Separability. Cambridge, MA: National Bureau of Economic Research, September 2018. http://dx.doi.org/10.3386/w25025.

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Samorodnitsky, Gennady. Integrability of Stable Processes. Fort Belvoir, VA: Defense Technical Information Center, June 1990. http://dx.doi.org/10.21236/ada225959.

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Glynn, Peter W., and Donald L. Iglehart. Consequences of Uniform Integrability for Simulation. Fort Belvoir, VA: Defense Technical Information Center, October 1986. http://dx.doi.org/10.21236/ada178860.

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Ramos Reina, Isaac, and Artemio González López. Integrability and entanglement in quantum systems. Fundación Avanza, May 2023. http://dx.doi.org/10.60096/fundacionavanza/1792022.

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Integrability, the Calogero model and its different versions and computation of the partition function of the PF spin chain via the "freezing trick". Entanglement and entanglement entropy. Application to a block of the XX spin chain.
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Lunin, Oleg. Integrability and Symmetries of Classical Geometries. Office of Scientific and Technical Information (OSTI), November 2021. http://dx.doi.org/10.2172/1830502.

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Vilasi, Gaetano. Nambu Dynamics, n-Lie Algebras and Integrability. GIQ, 2012. http://dx.doi.org/10.7546/giq-10-2009-265-278.

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Vilasi, Gaetano. Nambu Dynamics, n-Lie Algebras and Integrability. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-16-2009-77-91.

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Marmo, Giuseppe, Giovanni Sparano, and Gaetano Vilasi. Classical and Quantum Symmetries Reduction and Integrability. Journal of Geometry and Symmetry in Physics, 2013. http://dx.doi.org/10.7546/jgsp-31-2013-105-117.

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Sato, Hajime. Integrability of Contact Schwarzian Derivatives and its Linearization. GIQ, 2012. http://dx.doi.org/10.7546/giq-1-2000-225-228.

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Georgiev, Georgi. Non-integrability of a System with the Dyson Potential. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, September 2018. http://dx.doi.org/10.7546/crabs.2018.09.03.

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