The Principle of Least Action in Geometry and Dynamics

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.

List of contents

Aus dem Inhalt:
- 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.

Summary

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

• Authors: K. F. Siburg, Karl F. Siburg, Karl Friedrich Siburg
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 20.07.2004
• EAN: 9783540219446
• ISBN: 978-3-540-21944-6
• No. of pages: 132
• Dimensions: 154 mm x 235 mm x 9 mm
• Weight: 260 g
• Illustrations: XII, 132 p.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; B, Dynamics, Mathematics and Statistics, Differential Geometry, Numerical analysis, Manifolds (Mathematics), Dynamical Systems and Ergodic Theory, Ergodic theory, Dynamical systems, Global analysis (Mathematics), Global Analysis and Analysis on Manifolds, Differential & Riemannian geometry