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Hamiltonian ODE and Hamilton-Jacobi PDE with Stochastic Hamiltonian Function

Hamiltonian systems, from topology to applications through analysis II November 26, 2018 - November 30, 2018

November 26, 2018 (02:00 PM PST - 03:00 PM PST)
Speaker(s): Fraydoun Rezakhanlou (University of California, Berkeley)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Hamiton-Jacobi PDE

  • homogenization

  • Stationary Process

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
Video

3-Rezakhanlou

Abstract

In this talk I give an overview on the existing results for two questions associated with a Hamiltonian function that is selected randomly according to a probability measure that is translation invariant (this includes Hamiltonian functions that are almost periodic in position or in both position and momentum) 1. Consider a Hamiltonian ODE with a Hamiltonian function that is periodic in time. As in Arnold's conjecture we may wonder whether or not such an ODE has periodic orbits. 2. Analogously, we may study Hamilton-Jacobi PDEs and examine the question of homogenization that is closely related to the long time behavior of the solutions to the corresponding Hamiltonian ODE.

Supplements
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Video/Audio Files

3-Rezakhanlou

H.264 Video 3-Rezakhanlou.mp4 433 MB video/mp4 Download
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