Morse Theory for Hamiltonian Systems

by Alberto Abbondandolo

Overview

This Research Note explores existence and multiplicity questions for periodic solutions of first order, non-convex Hamiltonian systems. It introduces a new Morse (index) theory that is easier to use, less technical, and more flexible than existing theories and features techniques and results that, until now, have appeared only in scattered journals

Product Details

ISBN-13:	9781040218303
Publisher:	CRC Press
Publication date:	03/15/2001
Series:	Chapman & Hall/CRC Research Notes in Mathematics Series
Sold by:	Barnes & Noble
Format:	eBook
Pages:	208
File size:	507 KB

About the Author

Alberto Abbondandolo

Table of Contents

The Morse Index. The Relative Morse Index. Functional Setting. Superquadratic Hamiltonians. Asymptotically Linear Systems. The Arnold Conjectures for Symplectic Fixed Points. Index. References.

Editorial Reviews

Written for mathematicians working in nonlinear analysis, calculus of variations, Hamiltonian systems, and symplectic geometry, this study explores existence and multiplicity questions for periodic solutions of first order, non-convex Hamiltonian systems. It introduces a new Morse index theory that is less technical and more flexible than existing theories. Six chapters provide a self-contained treatment with full proofs. The purely abstract functional aspects have been separated from the applications to Hamiltonian systems, so that they may be applied in other areas of research as well. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"…provides an interesting introduction to index theories in the study of periodic solutions of Hamiltonian systems… the author presents some recently published results in the perspective of well-known ones and along the way he discusses several critical point techniques that could be useful in other problems."
- Mathematical Reviews 2002

From the Publisher