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Field name	Details
Dewey Class	516.36
Title	Index Theory for Symplectic Paths with Applications ([EBook] /) / by Yiming Long.
Author	Long, Yiming
Other name(s)	SpringerLink (Online service)
Publication	Basel : : Birkhäuser Basel : : Imprint: Birkhäuser, , 2002.
Physical Details	XXIV, 380 p. : online resource.
Series	Progress in mathematics 0743-1643 ; ; 207
ISBN	9783034881753
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-8175-3
Links to Related Works	Subject References: Differential Geometry . Mathematics . Authors: Long, Yiming . Corporate Authors: SpringerLink (Online service) . Series: Progress in mathematics . Classification: 516.36 .

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Index Theory for Symplectic Paths with Applications

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