Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise
Dynamical Systems
2024-09-19 v1 Probability
Abstract
We prove the positivity of Lyapunov exponents for the normal form of a Hopf bifurcation, perturbed by additive white noise, under sufficiently strong shear strength. This completes a series of related results for simplified situations which we can exploit by studying suitable limits of the shear and noise parameters. The crucial technical ingredient for making this approach rigorous is a result on the continuity of Lyapunov exponents via Furstenberg Khasminskii formulas.
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Cite
@article{arxiv.2212.06547,
title = {Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise},
author = {Dennis Chemnitz and Maximilian Engel},
journal= {arXiv preprint arXiv:2212.06547},
year = {2024}
}
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35 pages