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Horseshoes for a class of nonuniformly expanding random dynamical systems on the circle

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arxiv 2304.03685 v2 pith:S3TJ43RL submitted 2023-04-07 math.DS

Jeroen S.W. Lamb , Giuseppe Tenaglia , Dmitry Turaev This is my paper · ORCID
classification math.DS
keywords randomcircleclassdynamicalhorseshoesintervalsnoisepositive
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We propose a notion of random horseshoe for one-dimensional random dynamical systems. We prove the abundance of random horseshoes for a class of circle endomorphisms subject to additive noise, large enough to make the Lyapunov exponent positive. In particular, we provide conditions which guarantee that given any pair of disjoint intervals, for almost every noise realization, there exists a positive density sequence of return times to these intervals such that the induced dynamics are the full shift on two symbols.

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  1. Non uniform expansion and additive noise imply random horseshoe

    math.DS 2025-01 reject novelty 7.0 of 10

    Non-uniformly expanding maps with additive noise and a fully-positive-Lyapunov stationary measure are asserted to have dense random horseshoes, a random version of Smale's horseshoe.

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