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Rigidity For Infinitely Renormalizable Area-Preserving Maps
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Chalmers, Fraunhofer Chalmers Res Ctr Ind Math, S-41296 Gothenburg, Sweden..
SUNY Stony Brook, Dept Math, Stony Brook, NY 11794 USA..
2016 (English)In: Duke mathematical journal, ISSN 0012-7094, E-ISSN 1547-7398, Vol. 165, no 1, 129-159 p.Article in journal (Refereed) PublishedText
Abstract [en]

The period-doubling Cantor sets of strongly dissipative Henon-like maps with different average Jacobian are not smoothly conjugated, as was shown previously. The Jacobian rigidity conjecture says that the period-doubling Cantor sets of two-dimensional Henon-like maps with the same average Jacobian are smoothly conjugated. This conjecture is true for average Jacobian zero, for example, the one-dimensional case. The other extreme case is when the maps preserve area, for example, when the average Jacobian is one. Indeed, the main result presented here is that the period-doubling Cantor sets of area-preserving maps in the universality class of the Eckmann-Koch-Wittwer renormalization fixed point are smoothly conjugated.

Place, publisher, year, edition, pages
2016. Vol. 165, no 1, 129-159 p.
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URN: urn:nbn:se:uu:diva-277794DOI: 10.1215/00127094-3165327ISI: 000368565100004OAI: oai:DiVA.org:uu-277794DiVA: diva2:905767
Available from: 2016-02-23 Created: 2016-02-23 Last updated: 2016-02-23Bibliographically approved

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