Aperiodic and linearly repetitive Lorentz gases of finite horizon are not exponentially mixing

Rodrigo Treviño; Agnieszka Zelerowicz

doi:10.3934/dcds.2023057

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2023, Volume 43, Issue 9: 3549-3562. Doi: 10.3934/dcds.2023057

This issue Previous Article Minimality of $ \mathfrak{B} $-free systems in number fields Next Article

Aperiodic and linearly repetitive Lorentz gases of finite horizon are not exponentially mixing

Rodrigo Treviño^1, , and
Agnieszka Zelerowicz^2,

1.
University of Maryland, College Park, USA
2.
University of California, Riverside

^*Corresponding author: Rodrigo Treviño
^*Corresponding author: Rodrigo Treviño

Received: May 2022

Revised: April 2023

Early access: May 2023

Published: September 2023

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Abstract

We prove that aperiodic and linearly repetitive Lorentz gases with finite horizon are not mixing with exponential or stretched exponential speed in any dimension for any class of Hölder observables under a technical assumption known to hold in all known examples. We also bound the polynomial speed of mixing for observables in the Hölder space $ H_{\alpha} $ depending on $ \alpha $.

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Mathematics Subject Classification: Primary: 37C83, 37A25, 52C22.

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Figure 1. A trajectory in an aperiodic Lorentz gas

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