Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems
Dynamical Systems
2023-10-26 v1 Probability
Abstract
We confirm a long-standing conjecture concerning shear-induced chaos in stochastically perturbed systems exhibiting a Hopf bifurcation. The method of showing the main chaotic property, a positive Lyapunov exponent, is a computer-assisted proof. Using the recently developed theory of conditioned Lyapunov exponents on bounded domains and the modified Furstenberg-Khasminskii formula, the problem boils down to the rigorous computation of eigenfunctions of the Kolmogorov operators describing distributions of the underlying stochastic process.
Keywords
Cite
@article{arxiv.2101.01491,
title = {Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems},
author = {Maxime Breden and Maximilian Engel},
journal= {arXiv preprint arXiv:2101.01491},
year = {2023}
}