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arXiv · 1507.08191

Spectral gap and quantitative statistical stability for systems with contracting fibers and Lorenz-like maps

Stefano Galatolo·Rafael Lucena
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Abstract

We consider transformations preserving a contracting foliation, such that the associated quotient map satisfies a Lasota-Yorke inequality. We prove that the associated transfer operator, acting on suitable normed spaces, has a spectral gap (on which we have quantitative estimation). As an application we consider Lorenz-like two dimensional maps (piecewise hyperbolic with unbounded contraction and expansion rate): we prove that those systems have a spectral gap and we show a quantitative estimate for their statistical stability. Under deterministic perturbations of the system of size $\delta$, the physical measure varies continuously, with a modulus of continuity $O(\delta \log \delta )$, which is asymptotically optimal for this kind of piecewise smooth maps.

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Stefano Galatolo, Rafael Lucena. 2015-07-29. Spectral gap and quantitative statistical stability for systems with contracting fibers and Lorenz-like maps. https://doi.org/10.3934/dcds.2020079

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