EVENT DETAILS AND ABSTRACT

Title: Arnold diffusion for convex Hamiltonians in arbitrary degrees of freedom (joint with P. Bernard and K. Zhang)
Speaker: Vadim Kaloshin
Speaker Info: University of Maryland
Brief Description:
Special Note:
Abstract:

Arnold in the 1960's conjectured 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. 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.