The Principle of Least Action in Geometry and Dynamics / Edition 1

by Karl Friedrich Siburg

Overview

New variational methods by Aubry, Mather, and Mane, discovered in the last twenty years, gave deep insight into the dynamics of convex Lagrangian systems. This book shows how this Principle of Least Action appears in a variety of settings (billiards, length spectrum, Hofer geometry, modern symplectic geometry). Thus, topics from modern dynamical systems and modern symplectic geometry are linked in a new and sometimes surprising way. The central object is Mather’s minimal action functional. The level is for graduate students onwards, but also for researchers in any of the subjects touched in the book.

Product Details

ISBN-13:	9783540219446
Publisher:	Springer Berlin Heidelberg
Publication date:	07/12/2004
Series:	Lecture Notes in Mathematics , #1844
Edition description:	2004
Pages:	132
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

Aubry-Mather Theory.- Mather-Mané Theory.- The Minimal Action and Convex Billiards.- The Minimal Action Near Fixed Points and Invariant Tori.- The Minimal Action and Hofer's Geometry.- The Minimal Action and Symplectic Geometry.- References.- Index.