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Almost every interval translation map of three intervals is finite type
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2014 (English)In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 34, no 5, 2307-2314 p.Article in journal (Refereed) Published
Abstract [en]

Interval translation maps (ITMs) are a non-invertible generalization of interval exchange transformations (IETs). The dynamics of finite type ITMs is similar to IETs, while infinite type ITMs are known to exhibit new interesting effects. In this paper, we prove the finiteness conjecture for the ITMs of three intervals. Namely, the subset of ITMs of finite type contains an open, dense, and full Lebesgue measure subset of the space of ITMs of three intervals. For this, we show that any ITM of three intervals can be reduced either to a rotation or to a double rotation.

Place, publisher, year, edition, pages
2014. Vol. 34, no 5, 2307-2314 p.
Keyword [en]
Dynamical systems, attractors, interval translation maps, interval exchange maps, double rotations, color rotations
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-136467DOI: 10.3934/dcds.2014.34.2307ISI: 000326321700026Scopus ID: 2-s2.0-84886480076OAI: oai:DiVA.org:kth-136467DiVA: diva2:676471
Note

QC 20131206

Available from: 2013-12-06 Created: 2013-12-05 Last updated: 2017-12-06Bibliographically approved

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