For more information about this meeting, contact Nigel Higson.

Title: | Quasiergodic hypothesis and Arnold Diffusion in dimension 3 |

Seminar: | Department of Mathematics Colloquium |

Speaker: | Vadim Kaloshin, University of Maryland |

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 another joint with K. Zhang we prove strong form of Arnold's conjecture in dimension n=3. Jointly with M. Guardia we also prove a weak form of quasiergodic hypothesis. |

### Room Reservation Information

Room Number: | MB114 |

Date: | 03 / 06 / 2014 |

Time: | 03:35pm - 04:25pm |