Morse Theory For Hamiltonian Systems

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Morse Theory For Hamiltonian Systems

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Author : Alberto Abbondandolo
language : en
Publisher: CRC Press
Release Date : 2001-03-15

Morse Theory For Hamiltonian Systems written by Alberto Abbondandolo and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-15 with Mathematics categories.

This Research Note explores existence and multiplicity questions for periodic solutions of first order, non-convex Hamiltonian systems. It introduces a new Morse (index) theory that is easier to use, less technical, and more flexible than existing theories and features techniques and results that, until now, have appeared only in scattered journals

Infinite Dimensional Morse Theory And Multiple Solution Problems

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Author : K.C. Chang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Infinite Dimensional Morse Theory And Multiple Solution Problems written by K.C. Chang 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 2012-12-06 with Mathematics categories.

The book is based on my lecture notes "Infinite dimensional Morse theory and its applications", 1985, Montreal, and one semester of graduate lectures delivered at the University of Wisconsin, Madison, 1987. Since the aim of this monograph is to give a unified account of the topics in critical point theory, a considerable amount of new materials has been added. Some of them have never been published previously. The book is of interest both to researchers following the development of new results, and to people seeking an introduction into this theory. The main results are designed to be as self-contained as possible. And for the reader's convenience, some preliminary background information has been organized. The following people deserve special thanks for their direct roles in help ing to prepare this book. Prof. L. Nirenberg, who first introduced me to this field ten years ago, when I visited the Courant Institute of Math Sciences. Prof. A. Granas, who invited me to give a series of lectures at SMS, 1983, Montreal, and then the above notes, as the primary version of a part of the manuscript, which were published in the SMS collection. Prof. P. Rabinowitz, who provided much needed encouragement during the academic semester, and invited me to teach a semester graduate course after which the lecture notes became the second version of parts of this book. Professors A. Bahri and H. Brezis who suggested the publication of the book in the Birkhiiuser series.

Morse Theory And Floer Homology

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Author : Michèle Audin
language : en
Publisher:
Release Date : 2013-12-31

Morse Theory And Floer Homology written by Michèle Audin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-31 with categories.

Morse Theory And Hamiltonian Systems With Resonance At Infinity

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Author : S. B. Tshinanga
language : en
Publisher:
Release Date : 1986

Morse Theory And Hamiltonian Systems With Resonance At Infinity written by S. B. Tshinanga and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.

An Invitation To Morse Theory

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Author : Liviu Nicolaescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-02

An Invitation To Morse Theory written by Liviu Nicolaescu 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 2011-12-02 with Mathematics categories.

This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also be of interest to researchers. This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The reader is expected to have some familiarity with cohomology theory and differential and integral calculus on smooth manifolds. Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition.

Differential Geometry And Mathematical Physics

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Author : Gerd Rudolph
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-09

Differential Geometry And Mathematical Physics written by Gerd Rudolph 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 2012-11-09 with Science categories.

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.

Handbook Of Global Analysis

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Author : Demeter Krupka
language : en
Publisher: Elsevier
Release Date : 2011-08-11

Handbook Of Global Analysis written by Demeter Krupka and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-11 with Mathematics categories.

This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents

Morse Theory For Asymptotically Linear Hamiltonian Systems

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Author : Alberto Abbondandolo
language : en
Publisher:
Release Date : 1997

Morse Theory For Asymptotically Linear Hamiltonian Systems written by Alberto Abbondandolo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.

Handbook Of Differential Equations Ordinary Differential Equations

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Author : A. Canada
language : en
Publisher: Elsevier
Release Date : 2005-09-02

Handbook Of Differential Equations Ordinary Differential Equations written by A. Canada and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-02 with Mathematics categories.

This handbook is the second volume in a series devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, writtenby leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields, in order to make the chapters of the volume accessible to a wide audience. . Six chapters covering a variety of problems in ordinary differential equations. . Both, pure mathematical research and real word applications are reflected. Written by leading researchers in the area.

Topological And Variational Methods For Nonlinear Boundary Value Problems

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Author : Pavel Drabek
language : en
Publisher: CRC Press
Release Date : 1997-04-17

Topological And Variational Methods For Nonlinear Boundary Value Problems written by Pavel Drabek and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-04-17 with Mathematics categories.

In the rapidly developing area of nonlinear theory of differential equations, many important results have been obtained by the use of nonlinear functional analysis based on topological and variational methods. The survey papers presented in this volume represent the current state of the art in the subject. The methods outlined in this book can be used to obtain new results concerning the existence, uniqueness, multiplicity, and bifurcation of the solutions of nonlinear boundary value problems for ordinary and partial differential equations. The contributions to this volume are from well known mathematicians, and every paper contained in this book can serve both as a source of reference for researchers working in differential equations and as a starting point for those wishing to pursue research in this direction. With research reports in the field typically scattered in many papers within various journals, this book provides the reader with recent results in an accessible form.