Arnold Diffusion via Normally Hyperbolic Invariant Cylinders and Mather Variational Method, Part I

Arnold Diffusion via Normally Hyperbolic Invariant Cylinders and...Method, Part I - Vadim Kaloshin

Vadim Kaloshin
Pennsylvania State University; Member, School of Mathematics
March 7, 2012

In 1964 Arnold constructed an example of instabilities for nearly integrable systems and conjectured that generically this phenomenon takes place.
There has been big progress attacking this conjecture in the past decade. Jointly with Ke Zhang we present a new approach to this problem. It is based on a construction of crumpled and flower Normally Hyperbolic Invariant Cylinders. Once existence of these cylinders is shown to construct diffusion we apply Mather variational mechanism. A part of the project is also joint with P. Bernard.