## EVENT DETAILS AND ABSTRACT

**Analysis Seminar**
**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.

**Date:** Monday, October 11, 2010

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Prof. Jared Wunsch

**Contact email:** jwunsch@math.northwestern.edu

**Contact Phone:** 847-491-5580

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