arXiv:2212.06547 Abstract | arXiv Analytics

arXiv:2212.06547 [math.DS]Abstract References Reviews Resources

Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise

Published 2022-12-13Version 1

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.

Comments: 35 pages

Categories: math.DS, math.PR

Subjects: 37H15, 37H20

Keywords: hopf normal form, positive lyapunov exponent, additive noise, furstenberg khasminskii formulas, sufficiently strong shear strength

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