Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929502413651968 |
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| author | Chemnitz, Dennis Engel, Maximilian |
| author_facet | Chemnitz, Dennis Engel, Maximilian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06547 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise Chemnitz, Dennis Engel, Maximilian Dynamical Systems Probability 37H15, 37H20 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. |
| title | Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise |
| topic | Dynamical Systems Probability 37H15, 37H20 |
| url | https://arxiv.org/abs/2212.06547 |