Index Theory for Symplectic Paths with Applications
Index Theory for Symplectic Paths with Applications

Author: Yiming Long

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 393

ISBN-13: 3034881754

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This book gives an introduction to index theory for symplectic matrix paths and its iteration theory, as well as applications to periodic solution problems of nonlinear Hamiltonian systems. The applications of these concepts yield new approaches to some outstanding problems. Particular attention is given to the minimal period solution problem of Hamiltonian systems and the existence of infinitely many periodic points of the Poincaré map of Lagrangian systems on tori.

Index theory in nonlinear analysis
Index theory in nonlinear analysis

Author: Chungen Liu

Publisher: Springer

Published: 2019-05-22

Total Pages: 346

ISBN-13: 981137287X

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This book provides detailed information on index theories and their applications, especially Maslov-type index theories and their iteration theories for non-periodic solutions of Hamiltonian systems. It focuses on two index theories: L-index theory (index theory for Lagrangian boundary conditions) and P-index theory (index theory for P-boundary conditions). In addition, the book introduces readers to recent advances in the study of index theories for symmetric periodic solutions of nonlinear Hamiltonian systems, and for selected boundary value problems involving partial differential equations.

Progress in Variational Methods
Progress in Variational Methods

Author: Chungen Liu

Publisher: World Scientific

Published: 2010-09-07

Total Pages: 249

ISBN-13: 9814327832

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In the last forty years, nonlinear analysis has been broadly and rapidly developed. Lectures presented in the International Conference on Variational Methods at the Chern Institute of Mathematics in Tianjin of May 2009 reflect this development from different angles. This volume contains articles based on lectures in the following areas of nonlinear analysis: critical point theory, Hamiltonian dynamics, partial differential equations and systems, KAM theory, bifurcation theory, symplectic geometry, geometrical analysis, and celestial mechanics. Combinations of topological, analytical (especially variational), geometrical, and algebraic methods in these researches play important roles. In this proceedings, introductory materials on new theories and surveys on traditional topics are also given. Further perspectives and open problems on hopeful research topics in related areas are described and proposed. Researchers, graduate and postgraduate students from a wide range of areas in mathematics and physics will find contents in this proceedings are helpful.

Emerging Topics on Differential Equations and Their Applications
Emerging Topics on Differential Equations and Their Applications

Author: Hua Chen

Publisher: World Scientific

Published: 2012

Total Pages: 319

ISBN-13: 981444975X

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The aim of the SinoOCoJapan Conference of Young Mathematicians was to provide a forum for presenting and discussing recent trends and developments in differential equations and their applications, as well as to promote scientific exchanges and collaborations among young mathematicians both from China and Japan.The topics discussed in this proceedings include mean curvature flows, KAM theory, N-body problems, flows on Riemannian manifolds, hyperbolic systems, vortices, water waves, and reaction diffusion systems.

Emerging Topics On Differential Equations And Their Applications - Proceedings On Sino-japan Conference Of Young Mathematicians
Emerging Topics On Differential Equations And Their Applications - Proceedings On Sino-japan Conference Of Young Mathematicians

Author: Yiming Long

Publisher: World Scientific

Published: 2012-12-31

Total Pages: 319

ISBN-13: 9814449768

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The aim of the Sino-Japan Conference of Young Mathematicians was to provide a forum for presenting and discussing recent trends and developments in differential equations and their applications, as well as to promote scientific exchanges and collaborations among young mathematicians both from China and Japan.The topics discussed in this proceedings include mean curvature flows, KAM theory, N-body problems, flows on Riemannian manifolds, hyperbolic systems, vortices, water waves, and reaction diffusion systems.

Critical Point Theory and Its Applications
Critical Point Theory and Its Applications

Author: Wenming Zou

Publisher: Springer Science & Business Media

Published: 2006-09-10

Total Pages: 323

ISBN-13: 0387329684

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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.

Symplectic Geometry
Symplectic Geometry

Author: Helmut Hofer

Publisher: Springer Nature

Published: 2022-12-05

Total Pages: 1158

ISBN-13: 3031191110

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Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Rigid Analytic Geometry and Its Applications
Rigid Analytic Geometry and Its Applications

Author: Jean Fresnel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 303

ISBN-13: 1461200415

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Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," étale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the classroom or for self-study.

Introduction to Symplectic Topology
Introduction to Symplectic Topology

Author: Dusa McDuff

Publisher: Oxford University Press

Published: 2017

Total Pages: 637

ISBN-13: 0198794894

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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.

Stability and Bifurcation Theory for Non-Autonomous Differential Equations
Stability and Bifurcation Theory for Non-Autonomous Differential Equations

Author: Anna Capietto

Publisher: Springer

Published: 2012-12-14

Total Pages: 314

ISBN-13: 3642329063

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This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems. The courses took place during the C.I.M.E. Session "Stability and Bifurcation Problems for Non-Autonomous Differential Equations," held in Cetraro, Italy, June 19-25 2011. Anna Capietto and Jean Mawhin lectured on nonlinear boundary value problems; they applied the Maslov index and degree-theoretic methods in this context. Rafael Ortega discussed the theory of twist maps with nonperiodic phase and presented applications. Peter Kloeden and Sylvia Novo showed how dynamical methods can be used to study the stability/bifurcation properties of bounded solutions and of attracting sets for nonautonomous differential and functional-differential equations. The volume will be of interest to all researchers working in these and related fields.