Examples of nearly integrable systems with asymptotically dense projected orbits

Examples of nearly integrable systems with asymptotically dense projected orbits

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Jean-Pierre Marco, Universite Paris VI
Fine Hall 314

PLEASE NOTE SPECIAL TIME AND LOCATION.  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.