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Statistical stability and linear response for random hyperbolic dynamics

Part of: Random dynamical systems Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  07 December 2021

DAVOR DRAGIČEVIĆ  and
JULIEN SEDRO Open the ORCID record for JULIEN SEDRO [Opens in a new window]
DAVOR DRAGIČEVIĆ
Affiliation:
Department of Mathematics, University of Rijeka, Rijeka, Croatia (e-mail: ddragicevic@math.uniri.hr)
JULIEN SEDRO*
Affiliation:
Laboratoire de Probabilités, Statistique et Modélisation (LPSM), Sorbonne Université, Université de Paris, 4 Place Jussieu, 75005 Paris, France
*
e-mail: sedro@lpsm.paris
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Abstract

We consider families of random products of close-by Anosov diffeomorphisms, and show that statistical stability and linear response hold for the associated families of equivariant and stationary measures. Our analysis relies on the study of the top Oseledets space of a parametrized transfer operator cocycle, as well as ad-hoc abstract perturbation statements. As an application, we show that, when the quenched central limit theorem (CLT) holds, under the conditions that ensure linear response for our cocycle, the variance in the CLT depends differentiably on the parameter.

Keywords

linear responserandom dynamical systemsuniform hyperbolicity

MSC classification

Primary: 37D05: Hyperbolic orbits and sets 37H15: Multiplicative ergodic theory, Lyapunov exponents 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 2 , February 2023 , pp. 515 - 544
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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