Quantitative exponential mixing for the randomized Chirikov standard map

Ziyu Liu; Yankai Shi

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arXiv · 2605.20702

Quantitative exponential mixing for the randomized Chirikov standard map

Ziyu Liu·Yankai Shi

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Abstract

We investigate the mixing properties of a randomized Chirikov standard map on $\mathbb{T}^2$. While the deterministic dynamics exhibit obstructions to global ergodicity, we establish explicit almost-sure quantitative exponential mixing when kicking strengths are sufficiently large. To achieve this, we formulate a criterion for incompressible random dynamical systems, reducing quantitative exponential mixing to serval verifiable conditions. Additionally, we provide a milder parameter condition to derive qualitative exponential mixing and enhanced dissipation.

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Ziyu Liu, Yankai Shi. 2026-05-20. Quantitative exponential mixing for the randomized Chirikov standard map. https://arxiv.org/abs/2605.20702

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