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dc.contributor.authorAshwin, P
dc.contributor.authorGoetz, A
dc.contributor.authorPeres, P
dc.contributor.authorRodrigues, A
dc.date.accessioned2018-08-29T09:24:47Z
dc.date.issued2018-10-23
dc.description.abstractAlthough piecewise isometries (PWIs) are higher dimensional generalizations of one dimensional interval exchange transformations (IETs), their generic dynamical properties seem to be quite different. In this paper we consider embeddings of IET dynamics into PWI with a view to better understanding their similarities and differences. We derive some necessary conditions for existence of such embeddings using combinatorial, topological and measure theoretic properties of IETs. In particular, we prove that continuous embeddings of minimal 2-IETs into orientation preserving PWIs are necessarily trivial and that any 3-PWI has at most one non-trivially continuously embedded minimal 3-IET with the same underlying permutation. Finally, we introduce a family of 4-PWIs with apparent abundance of invariant nonsmooth fractal curves supporting IETs, that limit to a trivial embedding of an IET.en_GB
dc.identifier.citationPublished online 23 October 2018.en_GB
dc.identifier.doi10.1017/etds.2018.112
dc.identifier.urihttp://hdl.handle.net/10871/33834
dc.language.isoenen_GB
dc.publisherCambridge University Press (CUP)en_GB
dc.rights.embargoreasonUnder embargo until 23 April 2019 in compliance with publisher policy.en_GB
dc.rights© Cambridge University Press, 2018.
dc.titleEmbeddings of interval exchange transformations into planar piecewise isometriesen_GB
dc.typeArticleen_GB
dc.identifier.issn1469-4417
dc.descriptionThis is the author accepted manuscript. The final version is available from Cambridge University Press via the DOI in this record.en_GB
dc.identifier.journalErgodic Theory and Dynamical Systemsen_GB


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