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Recurrence and non‐ergodicity in generalized wind‐tree models
Author(s) -
Frączek Krzysztof,
Hubert Pascal
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600480
Subject(s) - ergodicity , tree (set theory) , lebesgue measure , measure (data warehouse) , mathematics , translation (biology) , flow (mathematics) , lebesgue integration , pure mathematics , statistical physics , mathematical analysis , computer science , statistics , physics , geometry , data mining , biochemistry , chemistry , messenger rna , gene
In this paper, we consider generalized wind‐tree models andZ d ‐covers over compact translation surfaces. Under suitable hypothesis, we prove the recurrence of the linear flow in a generic direction and the non‐ergodicity of Lebesgue measure.