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Quenched decay of correlations for random contracting Lorenz maps

Part of: Ergodic theory Low-dimensional dynamical systems

Published online by Cambridge University Press:  09 September 2025

ANDREW LARKIN  and
MARKS BOTIRBOYEVICH RUZIBOEV Open the ORCID record for MARKS BOTIRBOYEVICH RUZIBOEV [Opens in a new window]
ANDREW LARKIN
Affiliation:
Department of Mathematical Sciences, https://ror.org/04vg4w365Loughborough University , Loughborough, Leicestershire LE11 3TU, UK (e-mail: a.larkin2@lboro.ac.uk)
MARKS BOTIRBOYEVICH RUZIBOEV*
Affiliation:
V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9, University Street, Tashkent 100174, Uzbekistan Faculty of Mathematics, https://ror.org/03prydq77University of Vienna , Oskar Morgensternplatz 1, 1090 Vienna, Austria
*
e-mail: marx.ruziboev@gmail.com
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Abstract

In this work, we study rates of mixing for small independent and identically distributed random perturbations of contracting Lorenz maps sufficiently close to a Rovella parameter. By using a random Young tower construction, we prove that this random system has exponential decay of correlations.

Keywords

random dynamicslow dimensional dynamicsstatistical propertiesquenched decay of correllationrandom Young towers

MSC classification

Secondary: 37E05: Maps of the interval (piecewise continuous, continuous, smooth) 37A25: Ergodicity, mixing, rates of mixing

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , First View , pp. 1 - 58
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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