dc.contributor.author
Trujillo, Frank
dc.contributor.author
Ulcigari, C.
dc.date.accessioned
2025-07-04T09:41:32Z
dc.date.available
2025-07-04T09:41:32Z
dc.date.issued
2024-07-22
dc.identifier.uri
http://hdl.handle.net/2072/484502
dc.description.abstract
We produce affine interval exchange transformations (AIETs) which are topologically conjugated to (standard) interval exchange maps (IETs) via a singular conjugacy, i.e. a diffeomorphism h of [0,1] which is C0 but not C1 and such that the pull-back of the Lebesgue measure is a singular invariant measure for the AIET. In particular, we show that for almost every IET T0 of d ≥ 2 intervals and any vector ω belonging to the central-stable space Ecs(T0), for the Rauzy-Veech renormalization, any AIET T with log-slopes given by ω and semi-conjugated to T0 is topologically conjugated to T. In addition, if ω ∉ Es (T0), the conjugacy between T and T0 is singular.
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dc.description.sponsorship
Both au- thors acknowledge the support of the Swiss National Science Foundation through Grant 200021 188617{1. The rst author was partially supported by the Spanish State Re- search Agency, through the Severo Ochoa and Mar a de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M) and by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme Grant 101154283. The second author also acknowledges the support of support of the Swiss National Science Foundation through the SNSF Consolidator Grant 213663
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dc.format.extent
28 p.
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dc.publisher
Scuola Normale Superiore - Edizioni della Normale
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dc.relation.ispartof
Annali della Scuola Normale Superiore di Pisa -Classe di Scienze
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dc.rights
Attribution 4.0 International
*
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Affine interval exchange transformations
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dc.subject.other
Interval exchange maps
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dc.title
Affine interval exchange maps with a singular conjugacy to an IET
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/acceptedVersion
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dc.identifier.doi
10.2422/2036-2145.202305_001
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
