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Relevant bibliographies by topics / Symplectomorphisms

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Academic literature on the topic 'Symplectomorphisms'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 February 2022

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Journal articles on the topic "Symplectomorphisms"

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BIRAN, PAUL, MICHAEL ENTOV, and LEONID POLTEROVICH. "CALABI QUASIMORPHISMS FOR THE SYMPLECTIC BALL." Communications in Contemporary Mathematics 06, no. 05 (2004): 793–802. http://dx.doi.org/10.1142/s0219199704001525.

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We prove that the group of compactly supported symplectomorphisms of the standard symplectic ball admits a continuum of linearly independent real-valued homogeneous quasimorphisms. In addition these quasimorphisms are Lipschitz in the Hofer metric and have the following property: the value of each such quasimorphism on any symplectomorphism supported in any "sufficiently small" open subset of the ball equals the Calabi invariant of the symplectomorphism. By a "sufficiently small" open subset we mean that it can be displaced from itself by a symplectomorphism of the ball. As a byproduct we show

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Janeczko, Stanisław, and Zbigniew Jelonek. "Polynomial symplectomorphisms." Bulletin of the London Mathematical Society 40, no. 1 (2008): 108–16. http://dx.doi.org/10.1112/blms/bdm112.

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BESSA, MÁRIO, and JOÁO LOPES DIAS. "Hamiltonian suspension of perturbed Poincaré sections and an application." Mathematical Proceedings of the Cambridge Philosophical Society 157, no. 1 (2014): 101–12. http://dx.doi.org/10.1017/s0305004114000140.

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AbstractWe construct a Hamiltonian suspension for a given symplectomorphism which is the perturbation of a Poincaré map. This is especially useful for the conversion of perturbative results between symplectomorphisms and Hamiltonian flows in any dimension 2d. As an application, using known properties of area-preserving maps, we prove that for any Hamiltonian defined on a symplectic 4-manifold M and any point p ∈ M, there exists a C2-close Hamiltonian whose regular energy surface through p is either Anosov or contains a homoclinic tangency.

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Casals, Roger, Ailsa Keating, Ivan Smith, and Sylvain Courte. "Symplectomorphisms of exotic discs." Journal de l’École polytechnique — Mathématiques 5 (2018): 289–316. http://dx.doi.org/10.5802/jep.71.

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Entov, Michael. "Commutator length of symplectomorphisms." Commentarii Mathematici Helvetici 79, no. 1 (2004): 58–104. http://dx.doi.org/10.1007/s00014-001-0799-0.

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Pushkar’, P. E. "Generating functions of symplectomorphisms." Functional Analysis and Its Applications 28, no. 3 (1994): 198–201. http://dx.doi.org/10.1007/bf01078453.

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Barletta, Elisabetta, and Sorin Dragomir. "On boundary behaviour of symplectomorphisms." Kodai Mathematical Journal 21, no. 3 (1998): 285–305. http://dx.doi.org/10.2996/kmj/1138043941.

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Hellmann, Chris, Brennan Langenbach, and Michael VanValkenburgh. "Linear symplectomorphisms asR-Lagrangian subspaces." Involve, a Journal of Mathematics 8, no. 4 (2015): 551–69. http://dx.doi.org/10.2140/involve.2015.8.551.

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JANECZKO, STANISLAW, and ZBIGNIEW JELONEK. "LINEAR AUTOMORPHISMS THAT ARE SYMPLECTOMORPHISMS." Journal of the London Mathematical Society 69, no. 02 (2004): 503–17. http://dx.doi.org/10.1112/s0024610703004952.

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Uljarevic, Igor. "Viterbo’s transfer morphism for symplectomorphisms." Journal of Topology and Analysis 11, no. 01 (2019): 149–80. http://dx.doi.org/10.1142/s1793525319500079.

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We construct an analogue of Viterbo’s transfer morphism for Floer homology of an automorphism of a Liouville domain. As an application we prove that the Dehn–Seidel twist along any Lagrangian sphere in a Liouville domain of dimension [Formula: see text] has infinite order in the symplectic mapping class group.

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Dissertations / Theses on the topic "Symplectomorphisms"

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Lantzberg, Daniel [Verfasser], Hans-Georg [Akademischer Betreuer] Stark, Peter [Gutachter] Maaß, and Hans-Georg [Gutachter] Stark. "Quantum Frames and Uncertainty Principles arising from Symplectomorphisms / Daniel Lantzberg ; Gutachter: Peter Maaß, Hans-Georg Stark ; Betreuer: Hans-Georg Stark." Bremen : Staats- und Universitätsbibliothek Bremen, 2019. http://d-nb.info/1186248688/34.

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Deltour, Guillaume. "Propriétés symplectiques et hamiltoniennes des orbites coadjointes holomorphes." Phd thesis, Université Montpellier II - Sciences et Techniques du Languedoc, 2010. http://tel.archives-ouvertes.fr/tel-00552150.

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L'objet de cette thèse est l'étude de la structure symplectique des orbites coadjointes holomorphes, et de leurs projections. Une orbite coadjointe holomorphe O est une orbite coadjointe elliptique d'un groupe de Lie réel semi-simple, connexe, non compact et à centre fini, provenant d'un espace symétrique hermitien G/K, telle que O puisse être naturellement munie d'une structure kählérienne G-invariante. Ces orbites sont une généralisation de l'espace symétrique hermitien G/K. Dans cette thèse, nous prouvons que le symplectomorphisme de McDuff se généralise aux orbites coadjointes holomorphes,

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Rodríguez, Lito Edinson Bocanegra. "The method of exact algebraic restrictions." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-30102018-152753/.

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The aim of this work is to generalize the results given by Domitrz, Janeczko and Zhitomirskii in [10]. In this article they classify in the symplectic manifold (R2, w) where w = dx1 Λ dx2 + · · · + dx2n-1 Λ dx2n is the symplectic form given by Darbouxs Theorem, all the set which are symplectomorphic to a fixed quasi homogeneous curve . To do this classification they defined the algebraic restrictions. We develop a new method called the method of exact algebraic restrictions and show that this classification is solved for the non quasi homogeneous case N = {(x1, x2) = x≥3 = 0

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Bouzouina, Abelkader. "Comportement semi-classique de symplectomorphismes du tore quantifiés." Paris 9, 1997. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1997PA090021.

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Nous étudions dans cette thèse le comportement semi-classique de certaines transformations du tore bidimensionnel quantifiées. Nous traitons plus précisément les translations irrationnelles, les translations gauches, les automorphismes hyperboliques ainsi que les perturbations hamiltoniennes de ces dernières. Ces applications engendrent des dynamiques discrètes sur le tore qui sont, pour la mesure de Lebesgue, toutes ergodiques et faiblement mélangeantes en ce qui concerne les deux dernières. Les espaces de Hilbert quantiques associés au tore sont de dimension finie n ou l'entier n est inverse

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Blaier, Netanel S. "The quantum Johnson homomorphism and symplectomorphism of 3-folds." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/107327.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 345-354).<br>introduce a subset K2,A of the symplectic mapping class group, and an invariant ... that associates a characteristic class in Hochschild cohomology to every symplectomorphism ... K2,A. These are analogues to the familiar Johnson kernel X9 and second Johnson homomorphism - 2 from low-dimensional topology. The method is quite general, and unlike many abstract tools, explicitly computable in certain nice cases.

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Haro, Àlex. "The Primitive Function of an Exact Symplectomorphism. Variational principles, Converse KAM Theory and the problems of determination and interpolation." Doctoral thesis, Universitat de Barcelona, 1998. http://hdl.handle.net/10803/2116.

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We have divided this thesis in four parts:<br/><br/>a) PART I: Exact symplectic geometry (introduction of the problems). This part contains the basic tools of symplectic geometry and outlines the four subjects that we have study along the thesis: the determination problem, the interpolation problem, the variational problem and the breakdown problem.<br/><br/>b) PART II: On the standard symplectic manifold (analytical part). We recall the necessary tools to work on R(d) x R(d). That is we perform a coordinate treatment of the results. First of all we relate different kinds of generating functio

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Toko, Wilson Bombe. "Bundles in the category of Frölicher spaces and symplectic structure." Thesis, 2008. http://hdl.handle.net/10539/5860.

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Bundles and morphisms between bundles are defined in the category of Fr¨olicher spaces (earlier known as the category of smooth spaces, see [2], [5], [9], [6] and [7]). We show that the sections of Fr¨olicher bundles are Fr¨olicher smooth maps and the fibers of Fr¨olicher bundles have a Fr¨olicher structure. We prove in detail that the tangent and cotangent bundles of a n-dimensional pseudomanifold are locally diffeomorphic to the even-dimensional Euclidian canonical F-space R2n. We define a bilinear form on a finite-dimensional pseudomanifold. We show that the symplectic structure on a

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Books on the topic "Symplectomorphisms"

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McDuff, Dusa, and Dietmar Salamon. The group of symplectomorphisms. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0011.

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This chapter discusses the basic properties of the group of symplectomorphisms of a compact connected symplectic manifold and its subgroup of Hamiltonian symplectomorphisms. It begins by showing that the group of symplectomorphisms is locally path-connected and then moves on to the flux homomorphism. The main result here is a theorem of Banyaga that characterizes the Hamiltonian symplectomorphisms in terms of the flux homomorphism. In the noncompact case there is another interesting homomorphism, called the Calabi homomorphism, that takes values in the reals and may be defined on the universal

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McDuff, Dusa, and Dietmar Salamon. Symplectic manifolds. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0004.

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The third chapter introduces the basic notions of symplectic topology, such as symplectic forms, symplectomorphisms, and Lagrangian submanifolds. A fundamental classical construction is Moser isotopy, with its various applications such as Darboux’s theorem and the Lagrangian neighbourhood theorem. The chapter now includes a brief discussion of the Chekanov torus and Luttinger surgery. The last section on contact structures has been significantly expanded.

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McDuff, Dusa, and Dietmar Salamon. Area-preserving diffeomorphisms. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0009.

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This chapter is devoted to two-dimensional symplectomorphisms, which are just area- and orientation-preserving diffeomorphisms. The chapter includes an exposition of Birkhoff’s proof of Poincaré’s last geometric theorem, which asserts that an area-preserving twist map of the annulus must have at least 4 two distinct fixed points. It also discusses some applications of these ideas to billiard problems.

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McDuff, Dusa, and Dietmar Salamon. From classical to modern. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0002.

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The first chapter develops the basic concepts of symplectic topology from the vantage point of classical mechanics. It starts with an introduction to the Euler–Lagrange equation and shows how the Legendre transformation leads to Hamilton’s equations, symplectic forms, symplectomorphisms, and the symplectic action. It ends with a brief overview of some modern results in the subject on the symplectic topology of Euclidean space, such as the Weinstein conjecture and the Gromov nonsqueezing theorem.

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Mann, Peter. Poisson Brackets & Angular Momentum. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0017.

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This chapter discusses canonical transformations and gauge transformations and is divided into three sections. In the first section, canonical coordinate transformations are introduced to the reader through generating functions as the extension of point transformations used in Lagrangian mechanics, with the harmonic oscillator being used as an example of a canonical transformation. In the second section, gauge theory is discussed in the canonical framework and compared to the Lagrangian case. Action-angle variables, direct conditions, symplectomorphisms, holomorphic variables, integrable syste

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McDuff, Dusa, and Dietmar Salamon. Symplectic capacities. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0013.

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This chapter returns to the problems which were formulated in Chapter 1, namely the Weinstein conjecture, the nonsqueezing theorem, and symplectic rigidity. These questions are all related to the existence and properties of symplectic capacities. The chapter begins by discussing some of the consequences which follow from the existence of capacities. In particular, it establishes symplectic rigidity and discusses the relation between capacities and the Hofer metric on the group of Hamiltonian symplectomorphisms. The chapter then introduces the Hofer–Zehnder capacity, and shows that its existenc

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McDuff, Dusa, and Dietmar Salamon. Introduction to Symplectic Topology. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.001.0001.

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Over the past number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. In 1998, a significantly revised second edition contained new sections and updates. This third edition includes both further updates and new material on this fast-developing area. All chapters have been revised to

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Book chapters on the topic "Symplectomorphisms"

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Monterde, J. "Generalized symplectomorphisms." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0086428.

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de Gosson, Maurice A. "The Group of Hamiltonian Symplectomorphisms." In Symplectic Methods in Harmonic Analysis and in Mathematical Physics. Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-7643-9992-4_4.

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Eliashberg, Yakov, and Tudor Ratiu. "On the Diameter of the Symplectomorphism Group of the Ball." In Mathematical Sciences Research Institute Publications. Springer US, 1991. http://dx.doi.org/10.1007/978-1-4613-9719-9_10.

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Fehér, L., and C. Klimčík. "The Ruijsenaars Self-Duality Map as a Mapping Class Symplectomorphism." In Springer Proceedings in Mathematics & Statistics. Springer Japan, 2013. http://dx.doi.org/10.1007/978-4-431-54270-4_30.

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Fornæss, John Erik, and Nessim Sibony. "Holomorphic Symplectomorphisms in ℂ2." In Dynamical Systems and Applications. WORLD SCIENTIFIC, 1995. http://dx.doi.org/10.1142/9789812796417_0016.

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McDuff, Dusa. "A survey of the topological properties of symplectomorphism groups." In Topology, Geometry and Quantum Field Theory. Cambridge University Press, 2004. http://dx.doi.org/10.1017/cbo9780511526398.010.

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