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Journal articles on the topic 'Rational flowson the torus'

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Published: 4 June 2021
Last updated: 28 January 2023

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1

Muñoz, Vicente. "Torus rational fibrations." Journal of Pure and Applied Algebra 140, no. 3 (August 1999): 251–59. http://dx.doi.org/10.1016/s0022-4049(98)00004-8.

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2

Galaz-García, Fernando, Martin Kerin, Marco Radeschi, and Michael Wiemeler. "Torus Orbifolds, Slice-Maximal Torus Actions, and Rational Ellipticity." International Mathematics Research Notices 2018, no. 18 (March 24, 2017): 5786–822. http://dx.doi.org/10.1093/imrn/rnx064.

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3

LIENDO, ALVARO, and CHARLIE PETITJEAN. "UNIFORMLY RATIONAL VARIETIES WITH TORUS ACTION." Transformation Groups 24, no. 1 (November 4, 2017): 149–53. http://dx.doi.org/10.1007/s00031-017-9451-8.

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4

Gorsky, Eugene, Alexei Oblomkov, Jacob Rasmussen, and Vivek Shende. "Torus knots and the rational DAHA." Duke Mathematical Journal 163, no. 14 (November 2014): 2709–94. http://dx.doi.org/10.1215/00127094-2827126.

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5

Carotenuto, Alessandro, and Ludwik Dąbrowski. "Spin geometry of the rational noncommutative torus." Journal of Geometry and Physics 144 (October 2019): 28–42. http://dx.doi.org/10.1016/j.geomphys.2019.05.008.

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6

Neeb, Karl-Hermann. "On the Classification of Rational Quantum Tori and the Structure of Their Automorphism Groups." Canadian Mathematical Bulletin 51, no. 2 (June 1, 2008): 261–82. http://dx.doi.org/10.4153/cmb-2008-027-7.

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AbstractAn n-dimensional quantum torus is a twisted group algebra of the group ℤn. It is called rational if all invertible commutators are roots of unity. In the present note we describe a normal form for rational n-dimensional quantum tori over any field. Moreover, we show that for n = 2 the natural exact sequence describing the automorphism group of the quantum torus splits over any field.
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7

Ilten, Nathan, and Milena Wrobel. "Khovanskii-finite valuations, rational curves, and torus actions." Journal of Combinatorial Algebra 4, no. 2 (June 25, 2020): 141–66. http://dx.doi.org/10.4171/jca/41.

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8

Greenlees, J. P. C., and B. Shipley. "An algebraic model for rational torus-equivariant spectra." Journal of Topology 11, no. 3 (June 22, 2018): 666–719. http://dx.doi.org/10.1112/topo.12060.

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9

Brion, M. "Rational smoothness and fixed points of torus actions." Transformation Groups 4, no. 2-3 (June 1999): 127–56. http://dx.doi.org/10.1007/bf01237356.

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10

HO, CHOON-LIN. "W∞ AND SLq(2) ALGEBRAS IN THE LANDAU PROBLEM AND CHERN-SIMONS THEORY ON A TORUS." Modern Physics Letters A 10, no. 35 (November 20, 1995): 2665–73. http://dx.doi.org/10.1142/s0217732395002799.

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We discuss ω∞ and sl q(2) symmetries in Chern-Simons theory and Landau problem on a torus. It is shown that when the coefficient of the Chern-Simons term, or when the total flux passing through the torus is a rational number, there exist in general two w∞ and sl q(2) algebras, instead of one set each discussed in the literature. The general wave functions for the Landau problem with rational total flux is also presented.
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11

Hegna, C. C., and A. Bhattacharjee. "Islands in three-dimensional steady flows." Journal of Fluid Mechanics 227 (June 1991): 527–42. http://dx.doi.org/10.1017/s002211209100023x.

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We consider the problem of steady Euler flows in a torus. We show that in the absence of a direction of symmetry the solution for the vorticity contains δ-function singularities at the rational surfaces of the torus. We study the effect of a small but finite viscosity on these singularities. The solutions near a rational surface contain cat's eyes or islands, well known in the classical theory of critical layers. When the islands are small, their widths can be computed by a boundary-layer analysis. We show that the islands at neighbouring rational surfaces generally overlap. Thus, steady toroidal flows exhibit a tendency towards Beltramization.
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12

Scavia, Federico. "Retract Rationality and Algebraic Tori." Canadian Mathematical Bulletin 63, no. 1 (July 18, 2019): 173–86. http://dx.doi.org/10.4153/s0008439519000079.

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AbstractFor any prime number $p$ and field $k$, we characterize the $p$-retract rationality of an algebraic $k$-torus in terms of its character lattice. We show that a $k$-torus is retract rational if and only if it is $p$-retract rational for every prime $p$, and that the Noether problem for retract rationality for a group of multiplicative type $G$ has an affirmative answer for $G$ if and only if the Noether problem for $p$-retract rationality for $G$ has a positive answer for all $p$. For every finite set of primes $S$ we give examples of tori that are $p$-retract rational if and only if $p\notin S$.
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13

Li, Miao. "Abelian Chern-Simons theory and CFT of rational torus." Il Nuovo Cimento B 105, no. 10 (October 1990): 1113–17. http://dx.doi.org/10.1007/bf02827320.

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14

Bertram, Aaron. "Another way to enumerate rational curves with torus actions." Inventiones mathematicae 142, no. 3 (December 2000): 487–512. http://dx.doi.org/10.1007/s002220000094.

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15

Greenlees, J. P. C. "Rational torus-equivariant stable homotopy III: Comparison of models." Journal of Pure and Applied Algebra 220, no. 11 (November 2016): 3573–609. http://dx.doi.org/10.1016/j.jpaa.2016.05.001.

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16

Addas-Zanata, Salvador, and Patrice Le Calvez. "Rational mode locking for homeomorphisms of the $2$-torus." Proceedings of the American Mathematical Society 146, no. 4 (December 26, 2017): 1551–70. http://dx.doi.org/10.1090/proc/13793.

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17

JÄGER, T., and F. TAL. "Irrational rotation factors for conservative torus homeomorphisms." Ergodic Theory and Dynamical Systems 37, no. 5 (March 8, 2016): 1537–46. http://dx.doi.org/10.1017/etds.2015.112.

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We provide an equivalent characterization for the existence of one-dimensional irrational rotation factors of conservative torus homeomorphisms that are not eventually annular. It states that an area-preserving non-annular torus homeomorphism $f$ is semiconjugate to an irrational rotation $R_{\unicode[STIX]{x1D6FC}}$ of the circle if and only if there exists a well-defined speed of rotation in some rational direction on the torus, and the deviations from the constant rotation in this direction are uniformly bounded. By means of a counterexample, we also demonstrate that a similar characterization does not hold for eventually annular torus homeomorphisms.
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18

VASSILEVICH, D. V. "INDUCED CHERN–SIMONS ACTION ON NONCOMMUTATIVE TORUS." Modern Physics Letters A 22, no. 17 (June 7, 2007): 1255–63. http://dx.doi.org/10.1142/s0217732307023596.

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We compute a Chern–Simons term induced by the fermions on noncommutative torus interacting with two U(1) gauge fields. For rational noncommutativity θ∝P/Q we find a new mixed term in the action which involves only those fields which are (2π)/Q periodic, like the fields in a crystal with Q2nodes.
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19

NAZIR, SHAHEEN. "ON THE INTERSECTION OF RATIONAL TRANSVERSAL SUBTORI." Journal of the Australian Mathematical Society 86, no. 2 (April 2009): 221–31. http://dx.doi.org/10.1017/s1446788708000372.

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AbstractWe show that under a suitable transversality condition, the intersection of two rational subtori in an algebraic torus (ℂ*)n is a finite group which can be determined using the torsion part of some associated lattice. We also give applications to the study of characteristic varieties of smooth complex algebraic varieties. As an example we discuss A. Suciu’s line arrangement, the so-called deleted B3-arrangement.
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20

Combot, Thierry. "Rational integrability of trigonometric polynomial potentials on the flat torus." Regular and Chaotic Dynamics 22, no. 4 (July 2017): 386–407. http://dx.doi.org/10.1134/s1560354717040049.

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21

Kouptsov, K. L., J. H. Lowenstein, and F. Vivaldi. "Quadratic rational rotations of the torus and dual lattice maps." Nonlinearity 15, no. 6 (September 16, 2002): 1795–842. http://dx.doi.org/10.1088/0951-7715/15/6/306.

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22

Brion, M. "Erratum to "Rational Smoothness and Fixed Points of Torus Actions"." Transformation Groups 7, no. 1 (March 1, 2002): 107. http://dx.doi.org/10.1007/s00031-002-0007-0.

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23

Bregman, Corey. "Rational Growth and Almost Convexity of Higher-Dimensional Torus Bundles." International Mathematics Research Notices 2019, no. 13 (October 12, 2017): 4004–46. http://dx.doi.org/10.1093/imrn/rnx243.

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AbstractGiven a matrix $A\in SL(N,\mathbb{Z})$, form the semidirect product $G=\mathbb{Z}^N\rtimes_A \mathbb{Z}$ where the $\mathbb{Z}$-factor acts on $\mathbb{Z}^N$ by $A$. Such a $G$ arises naturally as the fundamental group of an $N$-dimensional torus bundle which fibers over the circle. In this article, we prove that if $A$ has distinct eigenvalues not lying on the unit circle, then there exists a finite index subgroup $H\leq G$ possessing rational growth series for some generating set. In contrast, we show that if $A$ has at least one eigenvalue not lying on the unit circle, then $G$ is not almost convex for any generating set.
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24

Brion, M. "Erratum to ?rational smoothness and fixed points of torus actions?" Transformation Groups 7, no. 1 (March 2002): 107. http://dx.doi.org/10.1007/bf01253468.

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25

Nassar, Ali, and Mark A. Walton. "Rational conformal field theory with matrix level and strings on a torus." Canadian Journal of Physics 92, no. 1 (January 2014): 65–70. http://dx.doi.org/10.1139/cjp-2013-0326.

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Study of the matrix-level affine algebra Um,K is motivated by conformal field theory and the fractional quantum Hall effect. Gannon completed the classification of Um,K modular-invariant partition functions. Here we connect the algebra U2,K to strings on 2-tori describable by rational conformal field theories. As Gukov and Vafa proved, rationality selects the complex-multiplication tori. We point out that the rational conformal field theories describing strings on complex-multiplication tori have characters and partition functions identical to those of the matrix-level algebra Um,K. This connection makes it obvious that the rational theories are dense in the moduli space of strings on Tm, and may prove useful in other ways.
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26

LIU, GENQIANG, and KAIMING ZHAO. "IRREDUCIBLE HARISH CHANDRA MODULES OVER THE DERIVATION ALGEBRAS OF RATIONAL QUANTUM TORI." Glasgow Mathematical Journal 55, no. 3 (February 25, 2013): 677–93. http://dx.doi.org/10.1017/s0017089512000845.

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AbstractLet d be a positive integer, q=(qij)d×d be a d×d matrix, ℂq be the quantum torus algebra associated with q. We have the semidirect product Lie algebra $\mathfrak{g}$=Der(ℂq)⋉Z(ℂq), where Z(ℂq) is the centre of the rational quantum torus algebra ℂq. In this paper, we construct a class of irreducible weight $\mathfrak{g}$-modules $\mathcal{V}$α (V,W) with three parameters: a vector α∈ℂd, an irreducible $\mathfrak{gl}$d-module V and a graded-irreducible $\mathfrak{gl}$N-module W. Then, we show that an irreducible Harish Chandra (uniformaly bounded) $\mathfrak{g}$-module M is isomorphic to $\mathcal{V}$α(V,W) for suitable α, V, W, if the action of Z(ℂq) on M is associative (respectively nonzero).
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27

SHEN, YUNZHU, and YONGXIANG ZHANG. "STRANGE NONCHAOTIC ATTRACTORS IN A QUASIPERIODICALLY-FORCED PIECEWISE SMOOTH SYSTEM WITH FAREY TREE." Fractals 27, no. 07 (November 2019): 1950118. http://dx.doi.org/10.1142/s0218348x19501184.

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The existence of strange nonchaotic attractors (SNAs) is verified in a simple quasiperiodically-forced piecewise smooth system with Farey tree. It can be seen that more and more jumping discontinuities appear on the smooth torus and the torus becomes extremely fragmented with the change of control parameter. Finally, the torus becomes an SNA with fractal property. In order to confirm the existence of SNAs in this system, we preliminarily use the estimation of the phase sensitivity exponent, estimation of the largest Lyapunov exponent and rational approximation. SNAs are further characterized by power spectra, recurrence plots, the largest Lyapunov exponents and their variance, the distribution of the finite-time Lyapunov exponents, the spectral distribution function and scaling laws.
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28

Zaslavski, Alexander J. "Generic uniqueness of a minimal solution for variational problems on a torus." Abstract and Applied Analysis 7, no. 3 (2002): 143–54. http://dx.doi.org/10.1155/s1085337502000842.

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We study minimal solutions for one-dimensional variational problems on a torus. We show that, for a generic integrand and any rational numberα, there exists a unique (up to translations) periodic minimal solution with rotation numberα.
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29

YIN, QIAN. "Lattès maps and combinatorial expansion." Ergodic Theory and Dynamical Systems 36, no. 4 (February 11, 2015): 1307–42. http://dx.doi.org/10.1017/etds.2014.125.

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A Lattès map $f:\widehat{\mathbb{C}}\rightarrow \widehat{\mathbb{C}}$ is a rational map that is obtained from a finite quotient of a conformal torus endomorphism. We characterize Lattès maps by their combinatorial expansion behavior.
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30

Herppich, Elaine. "On Fano Varieties with Torus Action of Complexity 1." Proceedings of the Edinburgh Mathematical Society 57, no. 3 (April 16, 2014): 737–53. http://dx.doi.org/10.1017/s0013091513000710.

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AbstractIn this work we provide effective bounds and classification results for rational ℚ-factorial Fano varieties with a complexity-one torus action and Picard number 1 depending on the two invariants dimension and Picard index. This complements earlier work by Hausenet al., where the case of a free divisor class group of rank 1 was treated.
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31

Kaneyama, Tamafumi. "Torus-equivariant vector bundles on projective spaces." Nagoya Mathematical Journal 111 (September 1988): 25–40. http://dx.doi.org/10.1017/s0027763000000982.

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For a free Z-module N of rank n, let T = TN be an n-dimensional algebraic torus over an algebraically closed field k defined by N. Let X = TN emb (Δ) be a smooth complete toric variety defined by a fan Δ (cf. [6]). Then T acts algebraically on X. A vector bundle E on X is said to be an equivariant vector bundle, if there exists an isomorphism ft: t*E → E for each k-rational point t in T, where t: X → X is the action of t. Equivariant vector bundles have T-linearizations (see Definition 1.2 and [2], [4]), hence we consider T-linearized vector bundles.
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32

Agapov, S. V. "Rational Integrals of a Natural Mechanical System on the 2-Torus." Siberian Mathematical Journal 61, no. 2 (March 2020): 199–207. http://dx.doi.org/10.1134/s0037446620020020.

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33

Etingof, Pavel, Eugene Gorsky, and Ivan Losev. "Representations of rational Cherednik algebras with minimal support and torus knots." Advances in Mathematics 277 (June 2015): 124–80. http://dx.doi.org/10.1016/j.aim.2015.03.003.

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34

Greenlees, J. P. C. "Rational torus-equivariant stable homotopy I: Calculating groups of stable maps." Journal of Pure and Applied Algebra 212, no. 1 (January 2008): 72–98. http://dx.doi.org/10.1016/j.jpaa.2007.05.010.

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35

Greenlees, J. P. C. "Rational torus-equivariant stable homotopy II: Algebra of the standard model." Journal of Pure and Applied Algebra 216, no. 10 (October 2012): 2141–58. http://dx.doi.org/10.1016/j.jpaa.2012.02.009.

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36

Rao, S. Eswara, Punita Batra, and Sachin S. Sharma. "The irreducible modules for the derivations of the rational quantum torus." Journal of Algebra 410 (July 2014): 333–42. http://dx.doi.org/10.1016/j.jalgebra.2014.03.024.

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37

Wang, Zhen, Ibrahim Ismael Hamarash, Payam Sadeghi Shabestari, and Sajad Jafari. "A New Megastable Oscillator with Rational and Irrational Parameters." International Journal of Bifurcation and Chaos 29, no. 13 (December 10, 2019): 1950176. http://dx.doi.org/10.1142/s0218127419501761.

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In this paper, a new two-dimensional nonlinear oscillator with an unusual sequence of rational and irrational parameters is introduced. This oscillator has endless coexisting limit cycles, which make it a megastable dynamical system. By periodically forcing this system, a new system is designed which is capable of exhibiting an infinite number of coexisting asymmetric torus and strange attractors. This system is implemented by an analog circuit, and its Hamiltonian energy is calculated.
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38

Cantat, Serge. "Caractérisation des exemples de Lattès et de Kummer." Compositio Mathematica 144, no. 5 (September 2008): 1235–70. http://dx.doi.org/10.1112/s0010437x08003576.

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AbstractLattès and Kummer examples are rational transformations of compact kähler manifolds that are covered by an affine transformation of a compact torus. We present a few ergodic characteristic properties of these examples. The main results concern the case of surfaces.
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39

Pandharipande, R., and A. Pixton. "Descendents on local curves: rationality." Compositio Mathematica 149, no. 1 (November 1, 2012): 81–124. http://dx.doi.org/10.1112/s0010437x12000498.

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AbstractWe study the stable pairs theory of local curves in 3-folds with descendent insertions. The rationality of the partition function of descendent invariants is established for the full local curve geometry (equivariant with respect to the scaling 2-torus), including relative conditions and odd-degree insertions for higher-genus curves. The capped 1-leg descendent vertex (equivariant with respect to the 3-torus) is also proven to be rational. The results are obtained by combining geometric constraints with a detailed analysis of the poles of the descendent vertex.
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40

TSUTSUMI, YASUYOSHI. "THE CASSON INVARIANT OF THE CYCLIC COVERING BRANCHED OVER SOME SATELLITE KNOT." Journal of Knot Theory and Its Ramifications 14, no. 08 (December 2005): 1029–44. http://dx.doi.org/10.1142/s0218216505004226.

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Let V be the standard solid torus in S3. Let Kp, 2 be the (p, 2)-torus knot in V such that Kp, 2 meets a meridian disk D of V in two points with the winding number zero and the 2-string tangle TKp, 2 obtained by cutting along D is a rational tangle. We compute the Casson invariant of the cyclic covering space of S3 branched over a satellite knot whose companion is any 2-bridge knot D(b1,…,b2m) and pattern is (V, Kp, 2).
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41

JONKER, LEO B., and LEI ZHANG. "Torus homeomorphisms whose rotation sets have empty interior." Ergodic Theory and Dynamical Systems 18, no. 5 (October 1998): 1173–85. http://dx.doi.org/10.1017/s0143385798117959.

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Let $F$ be a lift of a homeomorphism $f: {\Bbb T}^{2} \to {\Bbb T}^{2}$ homotopic to the identity. We assume that the rotation set $\rho(F)$ is a line segment with irrational slope. In this paper we use the fact that ${\Bbb T}^2$ is necessarily chain transitive under $f$ if $f$ has no periodic points to show that if $v \in \rho(F)$ is a rational point, then there is a periodic point $x \in {\Bbb T}^{2}$ such that $v$ is its rotation vector.
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42

LORENZ, MARTIN. "RATIONAL GROUP ACTIONS ON AFFINE PI-ALGEBRAS." Glasgow Mathematical Journal 55, A (October 2013): 101–11. http://dx.doi.org/10.1017/s0017089513000530.

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AbstractLet R be an affine PI-algebra over an algebraically closed field $\mathbb{k}$ and let G be an affine algebraic $\mathbb{k}$-group that acts rationally by algebra automorphisms on R. For R prime and G a torus, we show that R has only finitely many G-prime ideals if and only if the action of G on the centre of R is multiplicity free. This extends a standard result on affine algebraic G-varieties. Under suitable hypotheses on R and G, we also prove a PI-version of a well-known result on spherical varieties and a version of Schelter's catenarity theorem for G-primes.
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43

Burdak, Zbigniew, Marek Kosiek, Patryk Pagacz, Krzysztof Rudol, and Marek Słociński. "Generalized powers and measures." Opuscula Mathematica 41, no. 6 (2021): 747–54. http://dx.doi.org/10.7494/opmath.2021.41.6.747.

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Using the winding of measures on torus in "rational directions" special classes of unitary operators and pairs of isometries are defined. This provides nontrivial examples of generalized powers. Operators related to winding Szegö-singular measures are shown to have specific properties of their invariant subspaces.
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44

TAKAHASHI, S. "p-ADIC PERIODS OF MODULAR ELLIPTIC CURVES AND THE LEVEL-LOWERING THEOREM." International Journal of Number Theory 04, no. 01 (February 2008): 15–23. http://dx.doi.org/10.1142/s1793042108001183.

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An elliptic curve defined over the field of rational numbers can be considered as a complex torus. We can describe its complex periods in terms of integration of the weight-2 cusp form corresponding to the elliptic curve. In this paper, we will study an analogous description of the p-adic periods of the elliptic curve, considering the elliptic curve as a p-adic torus. An essential tool for the proof of such a description is the level-lowering theorem of Ribet, which is one of the main ingredients used in the proof of Fermat's Last Theorem.
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45

Deng, Yu, and Pierre Germain. "Growth of Solutions to NLS on Irrational Tori." International Mathematics Research Notices 2019, no. 9 (September 11, 2017): 2919–50. http://dx.doi.org/10.1093/imrn/rnx210.

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Abstract We prove polynomial bounds on the $H^s$ growth for the nonlinear Schrödinger equation set on a torus, in dimension 3, with super-cubic and sub-quintic nonlinearity. Due to improved Strichartz estimates, these bounds are better for irrational tori than they are for rational tori.
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46

DOEFF, H. ERIK. "Rotation measures for homeomorphisms of the torus homotopic to a Dehn twist." Ergodic Theory and Dynamical Systems 17, no. 3 (June 1997): 575–91. http://dx.doi.org/10.1017/s0143385797085015.

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We extend the theory of rotation vectors to homeomorphisms of the two-dimensional torus that are homotopic to a Dehn twist. We define a one-dimensional rotation number and recreate the theory of the homotopic case to the identity case. We prove that if such a map is area preserving and has mean rotation number zero, then it must have a fixed point. We prove that the rotation set is a compact interval, and that if the rotation interval contains two distinct numbers, then for any rational number in the rotation set there exists a periodic point with that rotation number. Finally, we prove that any interval with rational endpoints can be realized as the rotation set of a map homotopic to a Dehn twist.
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47

Golla, Marco, and Laura Starkston. "The symplectic isotopy problem for rational cuspidal curves." Compositio Mathematica 158, no. 7 (July 2022): 1595–682. http://dx.doi.org/10.1112/s0010437x2200762x.

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We define a suitably tame class of singular symplectic curves in 4-manifolds, namely those whose singularities are modeled on complex curve singularities. We study the corresponding symplectic isotopy problem, with a focus on rational curves with irreducible singularities (rational cuspidal curves) in the complex projective plane. We prove that every such curve is isotopic to a complex curve in degrees up to five, and for curves with one singularity whose link is a torus knot. Classification results of symplectic isotopy classes rely on pseudo-holomorphic curves together with a symplectic version of birational geometry of log pairs and techniques from four-dimensional topology.
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48

HOST, BERNARD. "Some results of uniform distribution in the multidimensional torus." Ergodic Theory and Dynamical Systems 20, no. 2 (April 2000): 439–52. http://dx.doi.org/10.1017/s0143385700000201.

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This paper contains a generalization to the $d$-torus $\mathbb{T}^d$ of earlier results (B. Host. Nombres normaux, entropie, translations. Israel J. Math. 91 (1995), 419–428). Given a probability measure $\mu$ on and an endomorphism $T$ of $\mathbb{T}^d$, we explore the relations between three properties: the uniform distribution of the sequence $(T^n\mathbf{t})$ for $\mu$-almost all $\mathbf{t}$; the behaviour of $\mu$ relative to the translations by some rational subgroups of $\mathbb{T}^d$; and the entropy of $\mu$ for another endomorphism $S$ of $\mathbb{T}^d$.
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49

Passeggi, Alejandro. "Rational polygons as rotation sets of generic homeomorphisms of the two torus." Journal of the London Mathematical Society 89, no. 1 (October 15, 2013): 235–54. http://dx.doi.org/10.1112/jlms/jdt040.

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50

Smyrnakis, Ioannis. "Boundary states, extended symmetry algebra, and module structure for certain rational torus models." Journal of Mathematical Physics 43, no. 12 (December 2002): 6085–95. http://dx.doi.org/10.1063/1.1517168.

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