Positive metric entropy arises between some KAM tori
Positive metric entropy arises between some KAM tori

Dong Chen , Penn State University)
Fine Hall 601
The celebrated KAM Theory says that if one makes a small perturbation of a nondegenerate completely integrable system, we still have a huge measure of invariant tori with quasiperiodic dynamics in the perturbed system. These invariant tori are known as KAM tori. What happens between KAM tori draws lots of attention. In this talk I will present a Lagrangian perturbation of the geodesic flow on a flat 3torus. The perturbation is C^m small (m can be arbitrarily large) but the flow has a positive measure of trajectories with positive Lyapunov exponent. The measure of this set is of course extremely small. Still, the flow has positive metric entropy. From this result we get positive metric entropy between some KAM tori.