DOCUMENTA MATHEMATICA, Extra Volume ICM III (1998), 223-235

Mark I. Freidlin

Title: Random and Deterministic Perturbations of Nonlinear Oscillators

Perturbations of Hamiltonian systems are considered. The long-time behavior of such a perturbed system, even in the case of deterministic perturbations, is governed, in general, by a stochastic process on a graph related to the Hamiltonian. We calculate the characteristics of the process for systems with one degree of freedom and consider some applications and generalizations.

1991 Mathematics Subject Classification: 60H10, 34F05, 35B20, 60J60

Keywords and Phrases: Random perturbations, Hamiltonian systems, PDE's with a small parameter

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