Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise

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...

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Bibliographic Details
Published inCommunications in mathematical physics Vol. 402; no. 2; pp. 1807 - 1843
Main Authors Chemnitz, Dennis, Engel, Maximilian
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2023
Springer Nature B.V
Subjects
Canonical forms
Classical and Quantum Gravitation
Complex Systems
Hopf bifurcation
Liapunov exponents
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Shear strength
Theoretical
White noise
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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-023-04764-z