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.
• Physical Description: XII, 132 p. online resource.
• ISBN: 9783540409854
• ISSN: 0075-8434 ;
• DOI: 10.1007/978-3-540-40985-4

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.