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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Rigidity for infinitely renormalizable areapreserving maps
 Duke mathematical journal 165 (2016), No.1, pp.129159 ISSN: 00127094 ISSN: 15477398 

 English 
 Journal Article 
 Fraunhofer FCC () 
Abstract
The perioddoubling Cantor sets of strongly dissipative Henonlike maps with different average Jacobian are not smoothly conjugated, as was shown previously. The Jacobian rigidity conjecture says that the perioddoubling Cantor sets of twodimensional Henonlike maps with the same average Jacobian are smoothly conjugated. This conjecture is true for average Jacobian zero, for example, the onedimensional 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 perioddoubling Cantor sets of areapreserving maps in the universality class of the EckmannKochWittwer renormalization fixed point are smoothly conjugated.