Relevant bibliographies by topics / Poincaré-Birkhoff theorem

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Academic literature on the topic 'Poincaré-Birkhoff theorem'

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Published: 14 March 2023

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Journal articles on the topic "Poincaré-Birkhoff theorem"

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Bonfiglioli, Andrea, and Roberta Fulci. "A New Proof of the Existence of Free Lie Algebras and an Application." ISRN Algebra 2011 (March 7, 2011): 1–11. http://dx.doi.org/10.5402/2011/247403.

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The existence of free Lie algebras is usually derived as a consequence of the Poincaré-Birkhoff-Witt theorem. Moreover, in order to prove that (given a set and a field of characteristic zero) the Lie algebra of the Lie polynomials in the letters of (over the field ) is a free Lie algebra generated by , all available proofs use the embedding of a Lie algebra into its enveloping algebra . The aim of this paper is to give a much simpler proof of the latter fact without the aid of the cited embedding nor of the Poincaré-Birkhoff-Witt theorem. As an application of our result and of a theorem due to Cartier (1956), we show the relationships existing between the theorem of Poincaré-Birkhoff-Witt, the theorem of Campbell-Baker-Hausdorff, and the existence of free Lie algebras.
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Michaelis, Walter. "The Dual Poincaré-Birkhoff-Witt Theorem." Advances in Mathematics 57, no. 2 (August 1985): 93–162. http://dx.doi.org/10.1016/0001-8708(85)90051-9.

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Berger, Roland. "The quantum Poincaré-Birkhoff-Witt theorem." Communications in Mathematical Physics 143, no. 2 (January 1992): 215–34. http://dx.doi.org/10.1007/bf02099007.

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Le Calvez, Patrice, and Jian Wang. "Some remarks on the Poincaré-Birkhoff theorem." Proceedings of the American Mathematical Society 138, no. 02 (October 7, 2009): 703–15. http://dx.doi.org/10.1090/s0002-9939-09-10105-3.

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Winkelnkemper, H. E. "A generalization of the Poincaré-Birkhoff theorem." Proceedings of the American Mathematical Society 102, no. 4 (April 1, 1988): 1028. http://dx.doi.org/10.1090/s0002-9939-1988-0934887-5.

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Kirillov, Alexander, and Victor Starkov. "Some extensions of the Poincaré–Birkhoff theorem." Journal of Fixed Point Theory and Applications 13, no. 2 (June 2013): 611–25. http://dx.doi.org/10.1007/s11784-013-0127-2.

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Margheri, Alessandro, Carlota Rebelo, and Fabio Zanolin. "Fixed points for planar maps with multiple twists, with application to nonlinear equations with indefinite weight." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2191 (January 4, 2021): 20190385. http://dx.doi.org/10.1098/rsta.2019.0385.

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In this paper, we investigate the dynamical properties associated with planar maps which can be represented as a composition of twist maps together with expansive–contractive homeomorphisms. The class of maps we consider present some common features both with those arising in the context of the Poincaré–Birkhoff theorem and those studied in the theory of topological horseshoes. In our main theorems, we show that the multiplicity results of fixed points and periodic points typical of the Poincaré–Birkhoff theorem can be recovered and improved in our setting. In particular, we can avoid assuming area-preserving conditions and we also obtain higher multiplicity results in the case of multiple twists. Applications are given to periodic solutions for planar systems of non-autonomous ODEs with sign-indefinite weights, including the non-Hamiltonian case. The presence of complex dynamics is also discussed. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.
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Franks, John. "Erratum to “Generalizations of the Poincaré–Birkhoff theorem”." Annals of Mathematics 164, no. 3 (November 1, 2006): 1097–98. http://dx.doi.org/10.4007/annals.2006.164.1097.

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Makar-Limanov, L. "A Version of the Poincaré-Birkhoff-Witt Theorem." Bulletin of the London Mathematical Society 26, no. 3 (May 1994): 273–76. http://dx.doi.org/10.1112/blms/26.3.273.

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Li, Yong, and Zheng Hua Lin. "A constructive proof of the Poincaré-Birkhoff theorem." Transactions of the American Mathematical Society 347, no. 6 (June 1, 1995): 2111–26. http://dx.doi.org/10.1090/s0002-9947-1995-1290734-4.

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Dissertations / Theses on the topic "Poincaré-Birkhoff theorem"

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Cloutier, John. "A Combinatorial Analog of the Poincaré–Birkhoff Fixed Point Theorem." Scholarship @ Claremont, 2003. https://scholarship.claremont.edu/hmc_theses/145.

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Results from combinatorial topology have shown that certain combinatorial lemmas are equivalent to certain topologocal fixed point theorems. For example, Sperner’s lemma about labelings of triangulated simplices is equivalent to the fixed point theorem of Brouwer. Moreover, since Sperner’s lemma has a constructive proof, its equivalence to the Brouwer fixed point theorem provides a constructive method for actually finding the fixed points rather than just stating their existence. The goal of this research project is to develop a combinatorial analogue for the Poincare ́-Birkhoff fixed point theorem.
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Herlemont, Basile. "Differential calculus on h-deformed spaces." Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0377/document.

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L'anneau $\Diff(n)$ des opérateurs différentiels $\h$-déformés apparaît dans la théorie des algèbres de réduction.Dans cette thèse, nous construisons les anneaux des opérateurs différentiels généralisés sur les espaces vectoriels $\h$-déformés de type $\gl$. Contrairement aux espaces vectoriels $q$-déformés pour lequel l'anneau des opérateurs différentiels est unique \`a isomorphisme pr\`es, l'anneau généralisé des opérateurs différentiels $\h$-déformés $\Diffs(n)$ est indexée par une fonction rationnelle $\sigma$ en $n$ variables, solution d'un syst\`eme d\'eg\'en\'er\'e d'\'equations aux diff\'erences finies. Nous obtenons la solution g\'en\'erale de ce syst\`eme. Nous montrons que le centre de $\Diffs(n)$ est un anneau des polynômes en $n$ variables. Nous construisons un isomorphisme entre des localisations de l'anneau $\Diffs(n)$ et de l’algèbre de Weyl $\text{W}_n$ l’étendue par $n$ indéterminés. Nous présentons des conditions irréductibilité des modules de dimension fini de $\Diffs(n)$. Finalement, nous discutons des difficultés a trouver les constructions analogues pour l'anneau $\Diff(n,N)$ correspondant \`a $N$ copies de $\Diff(n)$
The ring $\Diff(n)$ of $\h$-deformed differential operators appears in the theory of reduction algebras. In this thesis, we construct the rings of generalized differential operators on the $\h$-deformed vector spaces of $\gl$-type. In contrast to the $q$-deformed vector spaces for which the ring of differential operators is unique up to an isomorphism, the general ring of $\h$-deformed differential operators $\Diffs(n)$ is labeled by a rational function $\sigma$ in $n$ variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system. We show that the center of $\Diffs(n)$ is a ring of polynomials in $n$ variables. We construct an isomorphism between certain localizations of $\Diffs(n)$ and the Weyl algebra $\W_n$ extended by $n$ indeterminates. We present some conditions for the irreducibility of the finite dimensional $\Diffs(n)$-modules. Finally, we discuss difficulties for finding analogous constructions for the ring $\Diff(n, N)$ formed by several copies of $\Diff(n)$
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Book chapters on the topic "Poincaré-Birkhoff theorem"

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Fonda, Alessandro. "The Poincaré–Birkhoff Theorem." In Birkhäuser Advanced Texts Basler Lehrbücher, 213–29. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-47090-0_10.

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Hofer, Helmut, Alberto Abbondandolo, Urs Frauenfelder, and Felix Schlenk. "A generalized Poincaré–Birkhoff theorem." In Symplectic Geometry, 981–1024. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-19111-4_31.

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Positselski, Leonid. "The Poincaré–Birkhoff–Witt Theorem." In Relative Nonhomogeneous Koszul Duality, 77–108. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89540-2_4.

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Pascoletti, Anna, and Fabio Zanolin. "From the Poincaré–Birkhoff Fixed Point Theorem to Linked Twist Maps: Some Applications to Planar Hamiltonian Systems." In Differential and Difference Equations with Applications, 197–213. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7333-6_14.

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Dondè, Tobia, and Fabio Zanolin. "Multiple Periodic Solutions for a Duffing Type Equation with One-Sided Sublinear Nonlinearity: Beyond the Poincaré-Birkhoff Twist Theorem." In Differential and Difference Equations with Applications, 207–23. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56323-3_17.

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DING, WEI-YUE. "A GENERALIZATION OF THE POINCARÉ-BIRKHOFF THEOREM." In Peking University Series in Mathematics, 17–22. World Scientific, 2017. http://dx.doi.org/10.1142/9789813220881_0003.

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"A KAM theory for resonant tori and a generalization of Poincaré-Birkhoff fixed point theorem." In First International Congress of Chinese Mathematicians, 397–401. Providence, Rhode Island: American Mathematical Society, 2001. http://dx.doi.org/10.1090/amsip/020/35.

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Journal articles
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