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math.DSAug 8, 2023
authors
  • Andrew Larkin
  • Marks Ruziboev
institutions
  • Academy of Sciences Republic of Uzbekistan
  • Loughborough University
  • University of Vienna
arXiv abstractPDF
paper

Quenched decay of correlations for random contracting Lorenz maps

arXiv:2308.04351 · doi:10.1017/etds.2025.10215

Abstract

In this work, we consider i.i.d. random perturbations of contracting Lorenz maps sufficiently close to a Rovella parameter. We prove that the quenched correlations of the random dynamical system decay exponentially.

References in corpus (11)

  • Singular-hyperbolic attractors are chaotic
  • The Lorenz attractor is mixing
  • A spectral approach for quenched limit theorems for random expanding dynamical systems
  • Exponential decay of correlations for nonuniformly hyperbolic flows with a C^{1+α} stable foliation, including the classical Lorenz attractor
  • Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps
  • Limit theorems for random expanding or hyperbolic dynamical systems and vector-valued observables
  • Thermodynamic formalism for contracting Lorenz flows
  • On stochastic stability of non-uniformly expanding interval maps
  • Statistical stability and limit laws for Rovella maps
  • Statistical instability for contracting Lorenz flows
  • Quenched decay of correlations for nonuniformly hyperbolic random maps with an ergodic driving system
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