Ergodicity of explicit logarithmic cocycles over IETs

We prove ergodicity in a class of skew-product extensions of interval exchange transformations given by cocycles with logarithmic singularities. This, in particular, provides explicit examples of ergodic R-extensions of minimal locally Hamiltonian flows with non-degenerate saddles in genus two. More...

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Bibliographic Details
Authors: Berk, P., Trujillo, Frank, Ulcigrai, C.
Format: article
Publication Date:2025
Country:España
Institution:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repository:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/489105
Online Access:http://hdl.handle.net/2072/489105
Access Level:Open access
Keyword:Ergodicity
51
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spelling Ergodicity of explicit logarithmic cocycles over IETsBerk, P.Trujillo, FrankUlcigrai, C.Ergodicity51We prove ergodicity in a class of skew-product extensions of interval exchange transformations given by cocycles with logarithmic singularities. This, in particular, provides explicit examples of ergodic R-extensions of minimal locally Hamiltonian flows with non-degenerate saddles in genus two. More generally, given any symmetric irreducible permutation, we show that for almost every choice of lengths, the skew-product built over the associated IET using a cocycle with symmetric logarithmic singularities that is odd when restricted to each of the exchanged intervals is ergodic.The authors acknowledge the support of the Swiss National Science Foundation through Grant 200021_188617/1. The first author thanks the National Science Centre (Poland) grant OPUS 2022/45/B/ST1/00179. The second author acknowledges partial support by the UZH Postdoc Grant, grant no. FK-23-133 and by the Spanish State Research Agency, through the Severo Ochoa and Maria de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M).info:eu-repo/semantics/publishedVersionSpringer2025info:eu-repo/semantics/article45 p.application/pdfhttp://hdl.handle.net/2072/489105RECERCAT (Dipòsit de la Recerca de Catalunya)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésMathematische AnnalenAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2072/4891052026-05-29T05:05:01Z
dc.title.none.fl_str_mv Ergodicity of explicit logarithmic cocycles over IETs
title Ergodicity of explicit logarithmic cocycles over IETs
spellingShingle Ergodicity of explicit logarithmic cocycles over IETs
Berk, P.
Ergodicity
51
title_short Ergodicity of explicit logarithmic cocycles over IETs
title_full Ergodicity of explicit logarithmic cocycles over IETs
title_fullStr Ergodicity of explicit logarithmic cocycles over IETs
title_full_unstemmed Ergodicity of explicit logarithmic cocycles over IETs
title_sort Ergodicity of explicit logarithmic cocycles over IETs
dc.creator.none.fl_str_mv Berk, P.
Trujillo, Frank
Ulcigrai, C.
author Berk, P.
author_facet Berk, P.
Trujillo, Frank
Ulcigrai, C.
author_role author
author2 Trujillo, Frank
Ulcigrai, C.
author2_role author
author
dc.subject.none.fl_str_mv Ergodicity
51
topic Ergodicity
51
description We prove ergodicity in a class of skew-product extensions of interval exchange transformations given by cocycles with logarithmic singularities. This, in particular, provides explicit examples of ergodic R-extensions of minimal locally Hamiltonian flows with non-degenerate saddles in genus two. More generally, given any symmetric irreducible permutation, we show that for almost every choice of lengths, the skew-product built over the associated IET using a cocycle with symmetric logarithmic singularities that is odd when restricted to each of the exchanged intervals is ergodic.
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/2072/489105
url http://hdl.handle.net/2072/489105
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Mathematische Annalen
dc.rights.none.fl_str_mv Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 45 p.
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv RECERCAT (Dipòsit de la Recerca de Catalunya)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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