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arXiv · 1205.0826

Rigidity for infinitely renormalizable area-preserving maps

Denis Gaidashev·Tomas Johnson·Marco Martens
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Abstract

The period doubling Cantor sets of strongly dissipative Henon-like maps with different average Jacobian are not smoothly conjugated. 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, e.g. the one-dimensional case. The other extreme case is when the maps preserve area, e.g. the average Jacobian is one. Indeed, the period doubling Cantor set of area-preserving maps in the universality class of the Eckmann-Koch-Wittwer renormalization fixed point are smoothly conjugated.

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Denis Gaidashev, Tomas Johnson, Marco Martens. 2012-05-03. Rigidity for infinitely renormalizable area-preserving maps. https://doi.org/10.1215/00127094-3165327

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