Rigidity for Infinitely Renormalizable Area-preserving Maps
نویسندگان
چکیده
The period doubling Cantor sets of strongly dissipative Hénon-like maps with different average Jacobian are not smoothly conjugated. The Jacobian Rigidity Conjecture says that the period doubling Cantor sets of two-dimensional Hénon-like maps with the same average Jacobian are smoothly conjugated. This conjecture is true for average Jacobian zero, e.g. the onedimensional 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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