# Meeting Details

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