Overview

This text 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 Poincare 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.

Full Product Details

Author:   Yiming Long
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2002 ed.
Volume:   207
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   1.650kg
ISBN:  

9783764366476

ISBN 10:   3764366478
Pages:   380
Publication Date:   25 March 2002
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

I The Symplectic Group Sp(2n).- 1 Algebraic Aspects.- 2 Topological Aspects.- II The Variational Method.- 3 Hamiltonian Systems and Canonical Transformations.- 4 The Variational Functional.- III Index Theory.- 5 Index Functions for Symplectic Paths.- 6 Properties of Index Functions.- 7 Relations with other Morse Indices.- IV Iteration Theory.- 8 Precise Iteration Formulae.- 9 Bott-type Iteration Formulae.- 10 Iteration Inequalities.- 11 The Common Index Jump Theorem.- 12 Index Iteration Theory for Closed Geodesics.- V Applications.- 13 The Rabinowitz Conjecture.- 14 Periodic Lagrangian Orbits on Tori.- 15 Closed Characteristics on Convex Hypersurfaces.

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