Index Theory for Symplectic Paths with Applications

Yiming Long (Autor)

Buch | Softcover

XXIV, 380 Seiten

2012 | 1. Softcover reprint of the original 1st ed. 2002
Springer Basel (Verlag)
978-3-0348-9466-1 (ISBN)

Artikel merken

This book is based upon my monograph Index Theory for Hamiltonian Systems with Applications published in 1993 in Chinese, and my notes for lectures and courses given at Nankai University, Brigham Young University, ICTP-Trieste, and the Institute of Mathematics of Academia Sinica during the last ten years. The aim of this book is twofold: (1) to give an introduction to the index theory for symplectic matrix paths and its iteration theory, which form a basis for the Morse theoretical study on Hamilto nian systems, and to give applications of this theory to periodic boundary value problems of nonlinear Hamiltonian systems. Here the iteration theory means the index theory of iterations of periodic solutions and symplectic matrix paths. (2) to serve as a reference book on these topics. There are many different ways to introduce the index theory for symplectic paths in order to establish Morse type index theory of Hamiltonian systems. In this book, I have chosen a relatively elementary way, i.e., the homotopy classification method of symplectic matrix paths. It depends only on linear algebra, point set topology, and certain basic parts of linear functional analysis. I have tried to make this part of the book self-contained and at the same time include all of the major results on these topics so that researchers and students interested in them can read it without substantial difficulties, and can learn the main results in this area for their possible applications.

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.

Erscheint lt. Verlag	23.10.2012
Reihe/Serie	Progress in Mathematics
Zusatzinfo	XXIV, 380 p.
Verlagsort	Basel
Sprache	englisch
Maße	155 x 235 mm
Gewicht	623 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Boundary value problem • Functional Analysis • Index Theory • Perturbation • perturbation theory • Symplectic Geometry
ISBN-10	3-0348-9466-X / 303489466X
ISBN-13	978-3-0348-9466-1 / 9783034894661
Zustand	Neuware