For more information about this meeting, contact Dmitri Burago, Anatole Katok.

Title: | Arnold diffusion for convex Hamiltonians in arbitrary degrees of freedom (joint with P. Bernard and K. Zhang). |

Seminar: | Center for Dynamics and Geometry Seminars |

Speaker: | Vadim Kaloshin, Penn State |

Abstract: |

Arnold in 60th conjectures that for generic nearly integrable Hamiltonian systems
H_\epsilon(\theta,p)=H_0(p)+\epsilon H_1(\theta,p,t), \theta \in T^n, p\in R^n,
t \in T there are orbits whose action changes by a magnitude of order of one:
\[
|p(t)-p(0)|=O(1) \text{ independently of how small epsilon is}.
\]
We solve a version of this conjecture for convex Hamiltonians, by showing
that for typical perturbations O(1) is indeed independent of epsilon, only
depends on H_1. In the proof we combine ideas from theory of normal
forms, Conley's isolating block, and Mather variational method.
This is a joint work with P. Bernard and K. Zhang. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 02 / 07 / 2011 |

Time: | 03:35pm - 05:30pm |