Almost every interval translation map of three intervals is finite type
2014 (English)In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, Vol. 34, no 5, 2307-2314 p.Article in journal (Refereed) Published
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.
Dynamical systems, attractors, interval translation maps, interval exchange maps, double rotations, color rotations
IdentifiersURN: urn:nbn:se:kth:diva-136467DOI: 10.3934/dcds.2014.34.2307ISI: 000326321700026ScopusID: 2-s2.0-84886480076OAI: oai:DiVA.org:kth-136467DiVA: diva2:676471
QC 201312062013-12-062013-12-052013-12-06Bibliographically approved