Repository: Freie Universit├Ąt Berlin, Math Department

Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise

Chemnitz, Dennis and Engel, Maximilian (2022) Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise. arXive preprint . pp. 1-35. (Unpublished)

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Official URL: https://doi.org/10.48550/arXiv.2212.06547

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.

Item Type:Article
Subjects:Mathematical and Computer Sciences
Mathematical and Computer Sciences > Mathematics
Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2937
Deposited By: Monika Drueck
Deposited On:17 Apr 2023 09:44
Last Modified:17 Apr 2023 09:44

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