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On some generalizations of skew-shifts on T-2
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2019 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 39, p. 19-61Article in journal (Refereed) Published
Abstract [en]

In this paper we investigate maps of the two-torus T-2 of the form T (x, y) = (x + omega, g(x) + f (y)) for Diophantine omega is an element of T and for a class of maps f, g : T -> T, where each g is strictly monotone and of degree 2 and each f is an orientation-preserving circle homeomorphism. For our class of f and g, we show that T is minimal and has exactly two invariant and ergodic Borel probability measures. Moreover, these measures are supported on two T-invariant graphs. One of the graphs is a strange non-chaotic attractor whose basin of attraction consists of (Lebesgue) almost all points in T-2. Only a low-regularity assumption (Lipschitz) is needed on the maps f and g, and the results are robust with respect to Lipschitz-small perturbations of f and g.

Place, publisher, year, edition, pages
CAMBRIDGE UNIV PRESS , 2019. Vol. 39, p. 19-61
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-239960DOI: 10.1017/etds.2017.19ISI: 000451398100002Scopus ID: 2-s2.0-85018981635OAI: oai:DiVA.org:kth-239960DiVA, id: diva2:1269767
Funder
Swedish Research Council, 2012-3090
Note

QC 20181211

Available from: 2018-12-11 Created: 2018-12-11 Last updated: 2018-12-11Bibliographically approved

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