The Principle of Least Action in Geometry and Dynamics / by Karl Friedrich Siburg.

Format:

Book

Author/Creator:

Siburg, Karl Friedrich, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1844.

Lecture Notes in Mathematics, 0075-8434 ; 1844

Language:

English

Subjects (All):

Differentiable dynamical systems.

Global differential geometry.

Global analysis (Mathematics).

Dynamical Systems and Ergodic Theory.

Differential Geometry.

Global Analysis and Analysis on Manifolds.

Local Subjects:

Dynamical Systems and Ergodic Theory.

Differential Geometry.

Global Analysis and Analysis on Manifolds.

Physical Description:

1 online resource (XII, 132 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.

System Details:

text file PDF

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.

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.

Other Format:

Printed edition:

ISBN:

9783540409854

Access Restriction:

Restricted for use by site license.