Symplectic Topology And Measure Preserving Dynamical Systems

Author : Albert Fathi,Yong-Geun Oh,Claude Viterbo
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 47,7 Mb
Release : 2010-04-09
Category : Mathematics
ISBN : 9780821848920

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Symplectic Topology and Measure Preserving Dynamical Systems by Albert Fathi,Yong-Geun Oh,Claude Viterbo Pdf

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.

Author : Eduard Zehnder
Publisher : European Mathematical Society
Page : 372 pages
File Size : 55,5 Mb
Release : 2010
Category : Dynamics
ISBN : 3037190817

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Lectures on Dynamical Systems by Eduard Zehnder Pdf

This book originated from an introductory lecture course on dynamical systems given by the author for advanced students in mathematics and physics at ETH Zurich. The first part centers around unstable and chaotic phenomena caused by the occurrence of homoclinic points. The existence of homoclinic points complicates the orbit structure considerably and gives rise to invariant hyperbolic sets nearby. The orbit structure in such sets is analyzed by means of the shadowing lemma, whose proof is based on the contraction principle. This lemma is also used to prove S. Smale's theorem about the embedding of Bernoulli systems near homoclinic orbits. The chaotic behavior is illustrated in the simple mechanical model of a periodically perturbed mathematical pendulum. The second part of the book is devoted to Hamiltonian systems. The Hamiltonian formalism is developed in the elegant language of the exterior calculus. The theorem of V. Arnold and R. Jost shows that the solutions of Hamiltonian systems which possess sufficiently many integrals of motion can be written down explicitly and for all times. The existence proofs of global periodic orbits of Hamiltonian systems on symplectic manifolds are based on a variational principle for the old action functional of classical mechanics. The necessary tools from variational calculus are developed. There is an intimate relation between the periodic orbits of Hamiltonian systems and a class of symplectic invariants called symplectic capacities. From these symplectic invariants one derives surprising symplectic rigidity phenomena. This allows a first glimpse of the fast developing new field of symplectic topology.

Author : Dusa McDuff,Dietmar Salamon
Publisher : Oxford University Press
Page : 637 pages
File Size : 54,8 Mb
Release : 2017
Category : Mathematics
ISBN : 9780198794899

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Introduction to Symplectic Topology by Dusa McDuff,Dietmar Salamon Pdf

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.

Author : Ilia Itenberg,Burglind Jöricke,Mikael Passare
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 53,5 Mb
Release : 2011-12-13
Category : Mathematics
ISBN : 9780817682767

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Perspectives in Analysis, Geometry, and Topology by Ilia Itenberg,Burglind Jöricke,Mikael Passare Pdf

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.

Author : Kenji Fukaya,Yong-Geun Oh,Hiroshi Ohta,Kaoru Ono
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 54,9 Mb
Release : 2019-09-05
Category : Floer homology
ISBN : 9781470436254

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Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory by Kenji Fukaya,Yong-Geun Oh,Hiroshi Ohta,Kaoru Ono Pdf

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 .

Author : José Ignacio Cogolludo-Agustín,Eriko Hironaka
Publisher : American Mathematical Soc.
Page : 496 pages
File Size : 45,9 Mb
Release : 2011
Category : Algebraic topology
ISBN : 9780821848906

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Topology of Algebraic Varieties and Singularities by José Ignacio Cogolludo-Agustín,Eriko Hironaka Pdf

This volume contains invited expository and research papers from the conference Topology of Algebraic Varieties, in honour of Anatoly Libgober's 60th birthday, held June 22-26, 2009, in Jaca, Spain.

Author : Yong-Geun Oh
Publisher : Cambridge University Press
Page : 421 pages
File Size : 43,7 Mb
Release : 2015-08-27
Category : Mathematics
ISBN : 9781107072459

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Symplectic Topology and Floer Homology by Yong-Geun Oh Pdf

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.

Author : Vadim Kaloshin,Ke Zhang
Publisher : Princeton University Press
Page : 224 pages
File Size : 54,8 Mb
Release : 2020-11-03
Category : Science
ISBN : 9780691204932

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Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom by Vadim Kaloshin,Ke Zhang Pdf

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.

Author : J. P. Gossez,Denis Bonheure
Publisher : American Mathematical Soc.
Page : 278 pages
File Size : 42,8 Mb
Release : 2011
Category : Differential equations, Elliptic
ISBN : 9780821849071

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Nonlinear Elliptic Partial Differential Equations by J. P. Gossez,Denis Bonheure Pdf

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.

Author : Kurusch Ebrahimi-Fard
Publisher : American Mathematical Soc.
Page : 480 pages
File Size : 45,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853290

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Combinatorics and Physics by Kurusch Ebrahimi-Fard Pdf

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.

Author : Tewodros Amdeberhan,Luis A. Medina,Victor H. Moll
Publisher : American Mathematical Soc.
Page : 426 pages
File Size : 47,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821848692

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Gems in Experimental Mathematics by Tewodros Amdeberhan,Luis A. Medina,Victor H. Moll Pdf

These proceedings reflect the special session on Experimental Mathematics held January 5, 2009, at the Joint Mathematics Meetings in Washington, DC as well as some papers specially solicited for this volume. Experimental Mathematics is a recently structured field of Mathematics that uses the computer and advanced computing technology as a tool to perform experiments. These include the analysis of examples, testing of new ideas, and the search of patterns to suggest results and to complement existing analytical rigor. The development of a broad spectrum of mathematical software products, such as MathematicaR and MapleTM, has allowed mathematicians of diverse backgrounds and interests to use the computer as an essential tool as part of their daily work environment. This volume reflects a wide range of topics related to the young field of Experimental Mathematics. The use of computation varies from aiming to exclude human input in the solution of a problem to traditional mathematical questions for which computation is a prominent tool.

Author : Robert S. Doran, Paul J. Sally, Jr., and Loren Spice
Publisher : American Mathematical Soc.
Page : 294 pages
File Size : 55,6 Mb
Release : 2011
Category : Harmonic analysis
ISBN : 9780821874035

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Harmonic Analysis on Reductive, $p$-adic Groups by Robert S. Doran, Paul J. Sally, Jr., and Loren Spice Pdf

Author : Santiago Carrillo Menéndez,José Luis Fernández Pérez
Publisher : American Mathematical Soc.
Page : 158 pages
File Size : 41,8 Mb
Release : 2010
Category : Finance
ISBN : 9780821846735

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Mathematics in Finance by Santiago Carrillo Menéndez,José Luis Fernández Pérez Pdf

The paper by R. Zagst and M. Scherer is a short course on the different approaches used for pricing, hedging and risk management of credit derivatives. --

Author : Krzysztof Jarosz
Publisher : American Mathematical Soc.
Page : 256 pages
File Size : 51,5 Mb
Release : 2011-07-18
Category : Mathematics
ISBN : 9780821852514

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Function Spaces in Modern Analysis by Krzysztof Jarosz Pdf

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.

Author : Christian Houdré
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 54,7 Mb
Release : 2011
Category : Convexity spaces
ISBN : 9780821849712

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Concentration, Functional Inequalities and Isoperimetry by Christian Houdré Pdf

The interactions between concentration, isoperimetry and functional inequalities have led to many significant advances in functional analysis and probability theory. Important progress has also taken place in combinatorics, geometry, harmonic analysis and mathematical physics, with recent new applications in random matrices and information theory. This will appeal to graduate students and researchers interested in the interplay between analysis, probability, and geometry.