Lyapunov exponents for Hamiltonian systems under small Lévy-type perturbations

This work is to investigate the (top) Lyapunov exponent for a class of Hamiltonian systems under small non-Gaussian Lévy-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 ex...

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Veröffentlicht in:Chaos (Woodbury, N.Y.) N.Y.), 2021-08, Vol.31 (8), p.081101-081101
Hauptverfasser: Chao, Ying, Wei, Pingyuan, Duan, Jinqiao
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Duan, Jinqiao
description This work is to investigate the (top) Lyapunov exponent for a class of Hamiltonian systems under small non-Gaussian Lévy-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.
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subjects Chaos theory
Hamiltonian functions
Liapunov exponents
Perturbation
Smoothness
title Lyapunov exponents for Hamiltonian systems under small Lévy-type perturbations
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