The Principle of Least Action in Geometry and Dynamics

• Main Author: Siburg, Karl Friedrich (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.
• Edition: 1st ed. 2004.
• Series: Lecture Notes in Mathematics, 1844
• Subjects: Dynamics.; Ergodic theory.; Differential geometry.; Global analysis (Mathematics).; Manifolds (Mathematics).; Dynamical Systems and Ergodic Theory.; Differential Geometry.; Global Analysis and Analysis on Manifolds.

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 symplecti...

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.