dc.contributor.author | Ashwin, P | |
dc.contributor.author | Goetz, A | |
dc.contributor.author | Peres, P | |
dc.contributor.author | Rodrigues, A | |
dc.date.accessioned | 2018-08-29T09:24:47Z | |
dc.date.issued | 2018-10-23 | |
dc.description.abstract | Although 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.citation | Published online 23 October 2018. | en_GB |
dc.identifier.doi | 10.1017/etds.2018.112 | |
dc.identifier.uri | http://hdl.handle.net/10871/33834 | |
dc.language.iso | en | en_GB |
dc.publisher | Cambridge University Press (CUP) | en_GB |
dc.rights.embargoreason | Under embargo until 23 April 2019 in compliance with publisher policy. | en_GB |
dc.rights | © Cambridge University Press, 2018. | |
dc.title | Embeddings of interval exchange transformations into planar piecewise isometries | en_GB |
dc.type | Article | en_GB |
dc.identifier.issn | 1469-4417 | |
dc.description | This is the author accepted manuscript. The final version is available from Cambridge University Press via the DOI in this record. | en_GB |
dc.identifier.journal | Ergodic Theory and Dynamical Systems | en_GB |