On quasiergodic hypothesis and Arnold diffusion for nearly integrable systems 
Abstract: The famous ergodic hypothesis claims that a typical Hamiltonian dynamics on a typical energy surface is ergodic, however, KAM theory disproves this. It establishes a persistent set of positive measure of invariant KAM tori. The (weaker) quasiergodic hypothesis, proposed by Ehrenfest and Birkhoff, says that a typical Hamiltonian dynamics on a typical energy surface has a dense orbit. This question is wide open. In early 60th Arnold constructed an example of instabilities for a nearly integrable Hamiltonian of dimension n>2 and conjectured that this is a generic phenomenon, nowadays, called Arnold diffusion. In the last two decades a variety of powerful techniques to attack this problem were developed. In particular, Mather discovered a large class of invariant sets and a delicate variational technique to shadow them. During the talk we present a progress on proving Arnold diffusion and quasiergodic hypothesis. Here are arXiv links about this work: http://arxiv.org/abs/1212.1150 

Web page: Alexandru I. Suciu  Comments to: i.loseu@neu.edu  
Posted: November 7, 2014  URL: http://www.math.neu.edu/bhmn/kaloshin15.html 