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arXiv · 1705.05869

Exponential Law for Random Maps on Compact Manifolds

Nicolai Haydn·Jerome Rousseau·Fan Yang
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Abstract

We consider random dynamical systems on manifolds modeled by a skew product which have certain geometric properties and whose measures satisfy quenched decay of correlations at a sufficient rate. We prove that the limiting distribution for the hitting and return times to geometric balls are both exponential for almost every realisation. We then apply this result to random $C^2$ maps of the interval and random parabolic maps on the unit interval.

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Nicolai Haydn, Jerome Rousseau, Fan Yang. 2019-10-02. Exponential Law for Random Maps on Compact Manifolds. https://arxiv.org/abs/1705.05869

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