Author | Siburg, Karl Friedrich. author |
---|---|

Title | The Principle of Least Action in Geometry and Dynamics [electronic resource] / by Karl Friedrich Siburg |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004 |

Connect to | http://dx.doi.org/10.1007/978-3-540-40985-4 |

Descript | XII, 132 p. online resource |

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

CONTENT

Aubry-Mather Theory -- Mather-Manรฉ 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

Mathematics
Dynamics
Ergodic theory
Global analysis (Mathematics)
Manifolds (Mathematics)
Differential geometry
Mathematics
Dynamical Systems and Ergodic Theory
Differential Geometry
Global Analysis and Analysis on Manifolds