PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Federico Rodriguez Hertz, Anatole Katok, Mari Royer, Dmitri Burago.

Title:Random iterations of standard maps. ATTENTION: THIS IS CENTER FOR DYNAMICS AND GEOMETRY COLLOQUIUM
Seminar:Geometry Working Seminar
Speaker:Vadim Kaloshin, University of Maryland
Abstract:
In 1964 Arnold constructed an example of rotor and a pendulum with weak coupling such that it has orbits whose rotor action exhibits a change of order of one. This example is called Arnold's example and gave rise to so called Arnold diffusion. Numerical experiments show that for many initial conditions near the saddle of the pendulum rotor action exhibits diffusion process for Arnold's example. Proving this would justify the word ``diffusion'' for this phenomenon. One way to study Arnold example is to introduce an induced map also called a separatrix map. Treschev computed this map. A simplification of this separatrix map leads to the following model: Consider two nearly integrable standard maps with different potentials. We show that vertical component of random iteration of these maps satisfies the Central Limit Theorem. This is a joint work with Oriol Castejon.

Room Reservation Information

Room Number:MB114
Date:03 / 05 / 2014
Time:03:35pm - 04:35pm