For more information about this meeting, contact Federico Rodriguez Hertz, Anatole Katok, 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 |