Lyapunov exponents for Hamiltonian systems under small Levy-type perturbations

This work is to investigate the (top) Lyapunov exponent for a class of Hamiltonian systems under small non-Gaussian Levy-type noise with bounded jumps. In a suitable moving frame, the linearization of such a system can be regarded as a small perturbation of a nilpotent linear system. The Lyapunov exponent is then estimated by taking a Pinsky-Wihstutz transformation and applying the Khas'minskii formula, under appropriate assumptions on smoothness, ergodicity, and integrability. Finally, two examples are presented to illustrate our results.

Automated summary

This work investigates the (top) Lyapunov exponent for a class of Hamiltonian systems under small non-Gaussian Levy-type noise with bounded jumps, estimating it using a Pinsky-Wihstutz transformation and the Khas'minskii formula. The study presents results with appropriate assumptions on smoothness, ergodicity, and integrability, and illustrates them with two examples.