Morse Theory And Hamiltonian Systems With Resonance At Infinity
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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. Morse Theory for Hamiltonian Systems provides a detailed description of the Maslov index, introduces the notion of relative Morse index, and describes the functional setup for the variational theory of Hamiltonian systems, including a new proof of the equivalence between the Hamiltonian and the Lagrangian index. It also examines the superquadratic Hamiltonian, proving the existence of periodic orbits that do not necessarily satisfy the Rabinowitz condition, studies asymptotically linear systems in detail, and discusses the Arnold conjectures about the number of fixed points of Hamiltonian diffeomorphisms of compact symplectic manifolds. In six succinct chapters, the author provides a self-contained treatment with full proofs. The purely abstract functional aspects have been clearly separated from the applications to Hamiltonian systems, so many of the results can be applied in and other areas of current research, such as wave equations, Chern-Simon functionals, and Lorentzian geometry. Morse Theory for Hamiltonian Systems not only offers clear, well-written prose and a unified account of results and techniques, but it also stimulates curiosity by leading readers into the fascinating world of symplectic topology.
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.
S Minaire De Math Matique
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Author :
language : en
Publisher:
Release Date : 1986
S Minaire De Math Matique written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Geometrical Methods In Variational Problems
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Author : N.A. Bobylov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometrical Methods In Variational Problems written by N.A. Bobylov 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.
This self-contained monograph presents methods for the investigation of nonlinear variational problems. These methods are based on geometric and topological ideas such as topological index, degree of a mapping, Morse-Conley index, Euler characteristics, deformation invariant, homotopic invariant, and the Lusternik-Shnirelman category. Attention is also given to applications in optimisation, mathematical physics, control, and numerical methods. Audience: This volume will be of interest to specialists in functional analysis and its applications, and can also be recommended as a text for graduate and postgraduate-level courses in these fields.
Rapport
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Author :
language : en
Publisher:
Release Date : 1984
Rapport written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Topological Methods In Nonlinear Analysis
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Author :
language : en
Publisher:
Release Date : 2004
Topological Methods In Nonlinear Analysis written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Nonlinear functional analysis categories.
Topics In Critical Point Theory
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Author : Kanishka Perera
language : en
Publisher: Cambridge University Press
Release Date : 2012-11-01
Topics In Critical Point Theory written by Kanishka Perera 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 2012-11-01 with Mathematics categories.
This book introduces the reader to powerful methods of critical point theory and details successful contemporary approaches to many problems, some of which had proved resistant to attack by older methods. Topics covered include Morse theory, critical groups, the minimax principle, various notions of linking, jumping nonlinearities and the Fučík spectrum in an abstract setting, sandwich pairs and the cohomological index. Applications to semilinear elliptic boundary value problems, p-Laplacian problems and anisotropic systems are given. Written for graduate students and research scientists, the book includes numerous examples and presents more recent developments in the subject to bring the reader up to date with the latest research.
Critical Point Theory And Its Applications
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Author : Wenming Zou
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-10
Critical Point Theory And Its Applications written by Wenming Zou 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 2006-09-10 with Mathematics categories.
This book presents some of the latest research in critical point theory, describing methods and presenting the newest applications. Coverage includes extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. Applications described include Hamiltonian systems, Schrödinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations.
Nonlinearity
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Author :
language : en
Publisher:
Release Date : 2006-04
Nonlinearity written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04 with Mathematical analysis categories.
Topological Methods Variational Methods And Their Applications Proceedings Of The Icm2002 Satellite Conference On Nonlinear Functional Analysis
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Author : Haim Brezis
language : en
Publisher: World Scientific
Release Date : 2003-03-13
Topological Methods Variational Methods And Their Applications Proceedings Of The Icm2002 Satellite Conference On Nonlinear Functional Analysis written by Haim Brezis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-13 with Mathematics categories.
ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 14-18, 2002 at Taiyuan, Shanxi Province, China. This conference was organized by Mathematical School of Peking University, Academy of Mathematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University.166 mathematicians from 21 countries and areas in the world attended the conference. 53 invited speakers and 30 contributors presented their lectures. This conference aims at an overview of the recent development in nonlinear analysis. It covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrödinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.