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Approximating integrals with respect to stationary probability measures of iterated function systems

Part of: Dynamical systems with hyperbolic behavior Low-dimensional dynamical systems Approximation methods and numerical treatment of dynamical systems

Published online by Cambridge University Press:  08 June 2020

ITALO CIPRIANO  and
NATALIA JURGA
ITALO CIPRIANO
Affiliation:
Facultad de Matemáticas, Pontificia Universidad Católica de Chile (PUC), Avenida Vicuña Mackenna 4860, Santiago, Chile (e-mail: icipriano@gmail.com)
NATALIA JURGA
Affiliation:
Mathematical Institute, St Andrews, KY16 9SS, UK (e-mail: naj1@st-andrews.ac.uk)
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Abstract

We study fast approximation of integrals with respect to stationary probability measures associated to iterated function systems on the unit interval. We provide an algorithm for approximating the integrals under certain conditions on the iterated function system and on the function that is being integrated. We apply this technique to estimate Hausdorff moments, Wasserstein distances and Lyapunov exponents of stationary probability measures.

Keywords

low-dimensional dynamicsiterated function systemstransfer operatorstationary measures

MSC classification

Primary: 37M25: Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy) 37E05: Maps of the interval (piecewise continuous, continuous, smooth) 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
Secondary: 37D35: Thermodynamic formalism, variational principles, equilibrium states
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 8 , August 2021 , pp. 2294 - 2310
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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