Arnold diffusion and Mather theory

Ke Zhang
University of Toronto
April 11, 2018
Abstract: Arnold diffusion studies the problem of topological instability in nearly integrable Hamiltonian systems. An important contribution was made my John Mather, who announced a result in two and a half degrees of freedom and developed deep theory for its proof. We describe a recent effort to better conceptualize the proof for Arnold diffusion.

Diffusion along chains of normally hyperbolic cylinders

Marian Gidea
Yeshiva University
April 11, 2018
Abstract: We consider a geometric framework that can be applied to prove the existence of drifting orbits in the Arnold diffusion problem. The main geometric objects that we consider are 3-dimensional normally hyperbolic invariant cylinders with boundary, which admit well-defined stable and unstable manifolds. These enable us to define chains of cylinders i.e., finite, ordered families of cylinders in which each cylinder admits homoclinic connections, and any two consecutive cylinders admit heteroclinic connections.