Randomly perturbed dynamical systems and Aubry-Mather theory
by Fabio Camilli, Annalisa Cesaroni, Antonio Siconolfi
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 2, No. 3/4, 2009

Abstract: We give a new PDE proof of a Freidlin-Wentzell theorem about the exit points from a domain of a random process, obtained by perturbing a dynamical system through the addition of a small noise. The relevant part of the analysis concerns an Hamilton-Jacobi equation, coupled with a Neumann boundary condition, which does not possess any strict subsolution. A metric method based on the introduction of an intrinsic length is adopted, and a notion of Aubry set, adjusted to the setting, is given.

Online publication date: Wed, 20-Jan-2010

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