Random Iteration of Cylinder Maps and Stochasticity in Arnold's Example

Saturday, November 1, 2014 - 3:30pm - 4:30pm
Keller 3-180
Vadim Kaloshin (University of Maryland)
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 different integrable maps. We show that vertical component of random iteration of these maps converge to a diffusion process. This is a joint work with Oriol Castejon.
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