Rigidity for infinitely renormalizable area-preserving maps
| Autor: | Tomas Johnson, Denis Gaidashev, Marco Martens |
|---|---|
| Přispěvatelé: | Publica |
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Mathematics::Dynamical Systems General Mathematics Rigidity (psychology) Dynamical Systems (math.DS) Fixed point area-preserving maps 01 natural sciences renormalization Renormalization symbols.namesake FOS: Mathematics Mathematics - Dynamical Systems 0101 mathematics Mathematics 37E20 Conjecture 010102 general mathematics Zero (complex analysis) 37F25 Renormalization group period doubling 010101 applied mathematics rigidity Jacobian matrix and determinant Dissipative system symbols |
| Zdroj: | Duke Math. J. 165, no. 1 (2016), 129-159 |
| ISSN: | 0012-7094 |
| DOI: | 10.1215/00127094-3165327 |
| Popis: | 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. Comment: 55 pages, incl. references; 2 figures |
| Databáze: | OpenAIRE |
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