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Rigidity For Infinitely Renormalizable Area-Preserving Maps
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- Gaidashev, Denis (author)
- Uppsala universitet,Tillämpad matematik och statistik
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- Johnson, T. (author)
- Chalmers, Fraunhofer Chalmers Res Ctr Ind Math, S-41296 Gothenburg, Sweden.
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- Martens, M. (author)
- SUNY Stony Brook, Dept Math, Stony Brook, NY 11794 USA.
- (creator_code:org_t)
- Duke University Press, 2016
- 2016
- English.
- In: Duke mathematical journal. - : Duke University Press. - 0012-7094 .- 1547-7398. ; 165:1, s. 129-159
- Journal article (peer-reviewed)
Abstract
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
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- ref (subject category)
- art (subject category)
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