For more information about this meeting, contact Federico Rodriguez Hertz, Stephanie Zerby, Anatole Katok, Boris Kalinin, Dmitri Burago.

Title: | Arnold Diffusion via Invariant Cylinders and Mather Variational Method |

Seminar: | Center for Dynamics and Geometry Seminars |

Speaker: | Vadim Kaloshin, University of Maryland TWO HOUR TALK |

Abstract: |

The famous ergodic hypothesis claims that a typical Hamiltonian dynamics
on a typical energy surface is ergodic. However, KAM theory disproves this.
It establishes a persistent set of positive measure of invariant KAM tori.
The (weaker) quasi-ergodic hypothesis, proposed by Ehrenfest and Birkhoff,
says that a typical Hamiltonian dynamics on a typical energy surface has
a dense orbit. This question is wide open. In early 60th Arnold constructed
an example of instabilities for a nearly integrable Hamiltonian of
dimension $n>2$
and conjectured that this is a generic phenomenon, nowadays, called
Arnold diffusion.
In the last two decades a variety of powerful techniques to attack this problem
were developed. In particular, Mather discovered a large class of invariant sets
and a delicate variational technique to shadow them. In a series of preprints:
one joint with P. Bernard, K. Zhang and two with K. Zhang we prove Arnold's
conjecture in dimension $n=3$. |

### Room Reservation Information

Room Number: | MB114 |

Date: | 04 / 29 / 2013 |

Time: | 03:35pm - 05:35pm |