Random and deterministic perturbations of nonlinear oscillators
Perturbations of Hamiltonian systems are considered: \[ \dot p_t^\varepsilon= -f(q_t^\varepsilon)+\varepsilon\beta(p^\varepsilon_t,q^\varepsilon_t) +\sqrt{\varepsilon}\sigma(p^\varepsilon_t,q^\varepsilon_t)\circ\dot W_t,\qquad \dot q^\varepsilon_t=p^\varepsilon_t. \] The long-time behaviour is governed by a stochastic process on a graph related to the Hamiltonian system. The characteristics of the process for systems with one degree of freedom are calculated.
scientific article; zbMATH DE number 1184362