Index theory for symplectic paths with applications pdf epub mobi txt 電子書下載2025

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出版者:Birkhäuser Basel

作者:Yiming Long

出品人:

頁數:380

译者:

出版時間:2002-4-29

價格:1960

裝幀:Hardcover

isbn號碼:9783764366476

叢書系列:Progress in Mathematics

圖書標籤:

Index theory
Symplectic geometry
Symplectic paths
Morse theory
Critical point theory
Topology
Differential geometry
Mathematical physics
Calculus of variations
Geometric analysis

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具體描述

This book gives a systematic introduction to the index theory for symplectic matrix paths and its iteration theory, as well as applications to periodic solution problems of nonlinear Hamiltonian systems. Among the topics covered are the algebraic and topological properties of symplectic matrices and groups, the index theory for symplectic paths, relations with other Morse-type index theories, Bott-type iteration formulae, splitting numbers, precise index iteration formulae, various index iteration inequalities, and common index properties of finitely many symplectic paths. The applications of these concepts yield new approaches to some outstanding problems and important progress on their solutions. Particular attention is given to the minimal period solution problem of Hamiltonian systems, the existence of infinitely many periodic points of the Poincaré map of Lagrangian systems on tori, and the multiplicity and stability problems of closed characteristics on convex compact smooth hypersurfaces in 2n-dimensional euclidean vector space.

Researchers, graduate and postgraduate students from a wide range of areas inside mathematics or physics will benefit from this monograph. Teachers of advanced courses in symplectic geometry or Hamiltonian systems will also find it an excellent textbook.