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arXiv · 2101.01491

Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems

Maxime Breden·Maximilian Engel
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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.

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Maxime Breden, Maximilian Engel. 2021-01-05. Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems. https://doi.org/10.1214/22-aap1841

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