PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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
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