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On local rigidity of partially hyperbolic affine Z(k) actions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
CNRS IMJ PRG, Math UP7D 58 56, Ave France Boite Courrier 7012, F-75205 Paris, France..
2019 (English)In: Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, E-ISSN 1435-5345, Vol. 751, p. 1-26Article in journal (Refereed) Published
Abstract [en]

The following dichotomy for affine Z(k) actions on the torus T-d, k, d is an element of N, is shown to hold: (i) The linear part of the action has no rank-one factors, and then the affine action is locally rigid. (ii) The linear part of the action has a rank-one factor, and then the affine action is locally rigid in a probabilistic sense if and only if the rank-one factors are trivial. Local rigidity in a probabilistic sense means that rigidity holds for a set of full measure of translation vectors in the rank-one factors.

Place, publisher, year, edition, pages
WALTER DE GRUYTER GMBH , 2019. Vol. 751, p. 1-26
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Geometry
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URN: urn:nbn:se:kth:diva-270656DOI: 10.1515/crelle-2016-0059ISI: 000469511800001Scopus ID: 2-s2.0-85067100951OAI: oai:DiVA.org:kth-270656DiVA, id: diva2:1416879
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QC 20200325

Available from: 2020-03-25 Created: 2020-03-25 Last updated: 2020-03-25Bibliographically approved

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Damjanović, Danijela

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