The Principle of Least Action in Geometry and Dynamics

  • Authors
  • Karl Friedrich Siburg

Part of the Lecture Notes in Mathematics book series (LNM, volume 1844)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Karl Friedrich Siburg
    Pages 1-13
  3. Karl Friedrich Siburg
    Pages 15-35
  4. Karl Friedrich Siburg
    Pages 37-57
  5. Karl Friedrich Siburg
    Pages 81-95
  6. Karl Friedrich Siburg
    Pages 97-119
  7. Karl Friedrich Siburg
    Pages 121-125
  8. Back Matter
    Pages 127-128

About this book

Introduction

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.

Keywords

Lagrangian systems convex billiards lenth spectrum symplectic geometry variational principles

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-40985-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-21944-6
  • Online ISBN 978-3-540-40985-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book