Lyapunov Exponent and Stochastic Stability for Infinitely Renormalizable Lorenz Maps
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916859854454784 |
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| author | Ji, Haoyang Wang, Qihan |
| author_facet | Ji, Haoyang Wang, Qihan |
| contents | We prove that infinitely renormalizable contracting Lorenz maps with bounded geometry or the so-called {\it a priori bounds} satisfies the slow recurrence condition to the singular point $c$ at its two critical values $c_1^-$ and $c_1^+$. As the first application, we show that the pointwise Lyapunov exponent at $c_1^-$ and $c_1^+$ equals 0. As the second application, we show that such maps are stochastically stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05567 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lyapunov Exponent and Stochastic Stability for Infinitely Renormalizable Lorenz Maps Ji, Haoyang Wang, Qihan Dynamical Systems We prove that infinitely renormalizable contracting Lorenz maps with bounded geometry or the so-called {\it a priori bounds} satisfies the slow recurrence condition to the singular point $c$ at its two critical values $c_1^-$ and $c_1^+$. As the first application, we show that the pointwise Lyapunov exponent at $c_1^-$ and $c_1^+$ equals 0. As the second application, we show that such maps are stochastically stable. |
| title | Lyapunov Exponent and Stochastic Stability for Infinitely Renormalizable Lorenz Maps |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2412.05567 |