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arXiv · 2412.05567

Lyapunov Exponent and Stochastic Stability for Infinitely Renormalizable Lorenz Maps

Haoyang Ji·Qihan Wang
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Abstract

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.

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Haoyang Ji, Qihan Wang. 2024-12-07. Lyapunov Exponent and Stochastic Stability for Infinitely Renormalizable Lorenz Maps. https://arxiv.org/abs/2412.05567

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