A geometric mechanism for Arnold diffusion in the a priori stable case

Series: 
CDSNS Colloquium
Monday, September 21, 2015 - 11:00
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Yeshiva University
Organizer: 
We prove the existence of diffusion orbits drifting along heteroclinic chains of normally hyperbolic 3-dimensional cylinders, under suitable assumptions on the dynamics on the cylinders and on their homoclinic/heteroclinic connections. These assumptions are satisfied in the a priori stable case of the Arnold diffusion problem. We provide  a geometric argument that extends Birkhoff's procedure for constructing connecting orbits  inside a zone of instability for a twist map on the annuls. This is joint work with J.-P. Marco.