Symplectic Topology And Measure Preserving Dynamical Systems

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Symplectic Topology And Measure Preserving Dynamical Systems

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Author : Albert Fathi
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-04-09

Symplectic Topology And Measure Preserving Dynamical Systems written by Albert Fathi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-09 with Mathematics categories.

The papers in this volume were presented at the AMS-IMS-SIAM Joint Summer Research Conference on Symplectic Topology and Measure Preserving Dynamical Systems held in Snowbird, Utah in July 2007. The aim of the conference was to bring together specialists of symplectic topology and of measure preserving dynamics to try to connect these two subjects. One of the motivating conjectures at the interface of these two fields is the question of whether the group of area preserving homeomorphisms of the 2-disc is or is not simple. For diffeomorphisms it was known that the kernel of the Calabi invariant is a normal proper subgroup, so the group of area preserving diffeomorphisms is not simple. Most articles are related to understanding these and related questions in the framework of modern symplectic topology.

Introduction To Symplectic Topology

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Author : Dusa McDuff
language : en
Publisher: Oxford University Press
Release Date : 2017

Introduction To Symplectic Topology written by Dusa McDuff and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.

Over the last 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. This new third edition of a classic book in the feild includes updates and new material to bring the material right up-to-date.

Symplectic Topology And Floer Homology

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Author : Yong-Geun Oh
language : en
Publisher: Cambridge University Press
Release Date : 2015-08-27

Symplectic Topology And Floer Homology written by Yong-Geun Oh and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-27 with Mathematics categories.

The first part of a two-volume set offering a systematic explanation of symplectic topology. This volume covers the basic materials of Hamiltonian dynamics and symplectic geometry.

Perspectives In Analysis Geometry And Topology

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Author : Ilia Itenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-13

Perspectives In Analysis Geometry And Topology written by Ilia Itenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-13 with Mathematics categories.

The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.

Spectral Invariants With Bulk Quasi Morphisms And Lagrangian Floer Theory

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Author : Kenji Fukaya
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-05

Spectral Invariants With Bulk Quasi Morphisms And Lagrangian Floer Theory written by Kenji Fukaya and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-05 with Mathematics categories.

In this paper the authors first develop various enhancements of the theory of spectral invariants of Hamiltonian Floer homology and of Entov-Polterovich theory of spectral symplectic quasi-states and quasi-morphisms by incorporating bulk deformations, i.e., deformations by ambient cycles of symplectic manifolds, of the Floer homology and quantum cohomology. Essentially the same kind of construction is independently carried out by Usher in a slightly less general context. Then the authors explore various applications of these enhancements to the symplectic topology, especially new construction of symplectic quasi-states, quasi-morphisms and new Lagrangian intersection results on toric and non-toric manifolds. The most novel part of this paper is its use of open-closed Gromov-Witten-Floer theory and its variant involving closed orbits of periodic Hamiltonian system to connect spectral invariants (with bulk deformation), symplectic quasi-states, quasi-morphism to the Lagrangian Floer theory (with bulk deformation). The authors use this open-closed Gromov-Witten-Floer theory to produce new examples. Using the calculation of Lagrangian Floer cohomology with bulk, they produce examples of compact symplectic manifolds which admits uncountably many independent quasi-morphisms . They also obtain a new intersection result for the Lagrangian submanifold in .

Arnold Diffusion For Smooth Systems Of Two And A Half Degrees Of Freedom

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Author : Vadim Kaloshin
language : en
Publisher: Princeton University Press
Release Date : 2020-11-03

Arnold Diffusion For Smooth Systems Of Two And A Half Degrees Of Freedom written by Vadim Kaloshin and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-03 with Science categories.

The first complete proof of Arnold diffusion—one of the most important problems in dynamical systems and mathematical physics Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. In this groundbreaking book, Vadim Kaloshin and Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. Kaloshin and Zhang follow Mather's strategy but emphasize a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, this book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.

Nonlinear Elliptic Partial Differential Equations

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Author : J. P. Gossez
language : en
Publisher: American Mathematical Soc.
Release Date : 2011

Nonlinear Elliptic Partial Differential Equations written by J. P. Gossez and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

This volume contains papers on semi-linear and quasi-linear elliptic equations from the workshop on Nonlinear Elliptic Partial Differential Equations, in honor of Jean-Pierre Gossez's 65th birthday, held September 2-4, 2009 at the Universite Libre de Bruxelles, Belgium. The workshop reflected Gossez's contributions in nonlinear elliptic PDEs and provided an opening to new directions in this very active research area. Presentations covered recent progress in Gossez's favorite topics, namely various problems related to the $p$-Laplacian operator, the antimaximum principle, the Fucik Spectrum, and other related subjects. This volume will be of principle interest to researchers in nonlinear analysis, especially in partial differential equations of elliptic type.

Combinatorics And Physics

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Author : Kurusch Ebrahimi-Fard
language : en
Publisher: American Mathematical Soc.
Release Date : 2011

Combinatorics And Physics written by Kurusch Ebrahimi-Fard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

This book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany. Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity. In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.

Function Spaces In Modern Analysis

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Author : Krzysztof Jarosz
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-07-18

Function Spaces In Modern Analysis written by Krzysztof Jarosz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-18 with Mathematics categories.

This volume contains the proceedings of the Sixth Conference on Function Spaces, which was held from May 18-22, 2010, at Southern Illinois University at Edwardsville. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects.

Harmonic Analysis On Reductive P Adic Groups

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Author : Robert S. Doran, Paul J. Sally, Jr., and Loren Spice
language : en
Publisher: American Mathematical Soc.
Release Date : 2011

Harmonic Analysis On Reductive P Adic Groups written by Robert S. Doran, Paul J. Sally, Jr., and Loren Spice and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Harmonic analysis categories.