Examples of Nearly Integrable Systems with Asymptotically Dense Projected Orbits

Joint IAS-PU Symplectic Geometry Seminar
Topic:Examples of Nearly Integrable Systems with Asymptotically Dense Projected Orbits
Speaker:Jean-Pierre Marco
Affiliation:Universite Paris VI
Date:Friday, April 19
Time/Room:11:00am - 12:00pm/Fine Hall 314

The talk is intended to give examples of Arnold diffusion for nearly integrable systems which are very likely to be generic. We will describe an explicit perturbation of the flat metric on the three dimensional torus which admits orbits whose projection on their energy level become asymptotically dense in this level, when the size of the perturbation tends to 0. These examples can be seen as analogues of the initial Arnold model in which double resonances play the central role.