Title: Randomly perturbed dynamical systems and Aubry-Mather theory

Authors: Fabio Camilli, Annalisa Cesaroni, Antonio Siconolfi

Addresses: Dipartimento di Matematica Pura e Applicata, Universita di l'Aquila, loc. Monteluco di Roio, 67040 l'Aquila, Italy. ' Dipartimento di Matematica Pura e Applicata, Universita di Padova, via Trieste 63, 35131 Padova, Italy. ' Dipartimento di Matematica, Universita di Roma ''La Sapienza'', P.le Aldo Moro 2, 00185 Roma, Italy

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.

Keywords: dynamical systems; random perturbations; large deviations; viscosity solutions; PDE; partial differential equations; Aubry-Mather theory.

DOI: 10.1504/IJDSDE.2009.031100

International Journal of Dynamical Systems and Differential Equations, 2009 Vol.2 No.3/4, pp.139 - 169

Published online: 20 Jan 2010 *

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