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non-uniformly hyperbolic system

Ergodic Theory and Dynamical Systems (1)

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Wasserstein convergence rates in the invariance principle for deterministic dynamical systems
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ZHENXIN LIU, ZHE WANG
Journal:

Ergodic Theory and Dynamical Systems / Volume 44 / Issue 4 / April 2024

Published online by Cambridge University Press:

13 June 2023, pp. 1172-1191

Print publication:

April 2024
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In this paper, we consider the convergence rate with respect to Wasserstein distance in the invariance principle for deterministic non-uniformly hyperbolic systems. Our results apply to uniformly hyperbolic systems and large classes of non-uniformly hyperbolic systems including intermittent maps, Viana maps, unimodal maps and others. Furthermore, as a non-trivial application to the homogenization problem, we investigate the Wasserstein convergence rate of a fast–slow discrete deterministic system to a stochastic differential equation.