Quantitative statistical stability and convergence to equilibrium. An application to maps with indifferent fixed points

We show a general relation between fixed point stability of suitably perturbed transfer operators and convergence to equilibrium (a notion which is strictly related to decay of correlations). We apply this relation to deterministic perturbations of a large class of maps with indifferent fixed points...

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Published in:Chaos, solitons and fractals solitons and fractals, 2017-10, Vol.103, p.596-601
Main Author: Galatolo, Stefano
Format: Article
Language:English
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Summary:We show a general relation between fixed point stability of suitably perturbed transfer operators and convergence to equilibrium (a notion which is strictly related to decay of correlations). We apply this relation to deterministic perturbations of a large class of maps with indifferent fixed points. It turns out that the L1 dependence of the a.c.i.m. on small suitable deterministic changes for these kind of maps is Hölder, with an exponent which is explicitly estimated.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2017.07.005