Topological obstructions to smoothness for infinitely renormalizable maps of the disc

Nonlinearity

Volumn 17, Issue 5, 2004, Pages 1547-1569

  Moreira, F J ^a  

^a UNIVERSITY OF PORTO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4644236202     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/17/5/001     Document Type: Article

References (26)

1. Birman J 1984 Braids, links and mapping class group Ann. Math Stud. vol 4 (Princeton, NJ: Princeton University Press)
2. Bowen R and Franks J 1987 Invariant circles and the order structure of periodic orbits in monotone twist maps Topology 26 21-35
3. Boyland P and Hall G 1976 The periodic points of maps of the disk and the interval Topology 15 337-42
4. Campanino M, Epstein H and Ruelle D 1981 On the existence of the Feigenbaum's fixed point Commun. Math. Phys. 79 261-302
5. Campanino M and Epstein H 1982 On Feigenbaum's functional equation g g(λx) + λg(x) = 0 Topology 21 125-9
6. Catsigeras E 1994 Cascades of period doubling of stable codimension one IMPA's Thesis
7. Catsigeras E, Gambaudo J-M and Moreira F 1998 Infinitely renormalizable diffeomorphisms of the disk at the boundary of chaos Proc. Am. Math. Soc. 126 297-304
8. n J. Stat. Phys. 25 1-15
9. Coullet P and Tresser C 1978 Itérations d'endomorphismes et groupe de renormalisation J. Phys. C: Solid State 525-8
10. Coullet P and Tresser C 1978 Itérations d'endomorphismes et groupe de renormalisation C. R. Acad. Sci. Paris A 287 577-80
11. Courcelle O 1996 Cascades d'orbites périodiques en dimension 1 et 2: hyperbolicité et renormalisaton Thesis Université de Nice-Sophia Antipolis
12. Eckman J-P and Wittwer P 1987 A complete proof of the Feigenbaum conjectures J. Stat. Phys. 46 455-75
13. 2 Kupka-Smale diffeomorphism of the disk with no sorces or sinks Dynamical Systems and Turbulence (Lecture Notes in Mathematics vol 898) pp 90-8
14. Franks J and Young L S 1978 Quantitative universality for a class of non-linear transformations J. Stat. Phys. 19 25-52
15. Gambaudo J-M 1991 Boundary of Morse-Smale surface diffeomorphisms: an obstruction to smoothness Proc. Int. Conf. on Dynamical Systems and Related Topics (Advanced Series in Dynamical Systems) vol 9 (London: World Scientific) pp 141-52
16. 2 with neither sinks nor sources Nonlinearity 2 287-304
17. 2 with topological entropy zero Ann. Inst. H Poincaré 49 335-46
18. Gambaudo J-M, Sullivan D and Tresser C 1994 Infinite cascades of braids and smooth dynamical systems Topology 33 85-94
19. Gambaudo J-M and Tresser C 1991 How horseshoes are created Instabilities and Nonequilibrium Structures III ed E Tirapegui and W Zeller (Dordrecht: Reidel)
20. Gambaudo J-M and Tresser C 1992 Self-similar constructions in smooth dynamics. Smoothness and dimension Commun. Math. Phys. 150 45-58
21. Lanford O E III 1982 A computer-assisted proof of the Feigenbaum conjecure Bull. Am. Math. Soc. 6 427-34
22. Lyubich M 1999 Feigenbaum-Coullet-Tresser universality and Milnor's hairiness conjecture Ann. Math. 149 319-420
23. de Melo W and van Strien S 1993 One-Dimensional Dynamics (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge vol 25) (Berlin: Spinger)
24. McMullen C 1996 Renormalization and 3-manifolds which fiber over the circle Ann. Math. Stud. vol 142 (Princeton, NJ: Princeton University Press)
25. Smania D 2001 Complex bounds for multimodal maps: bounded combinatorics Nonlinearity 14 1311-30
26. Sullivan D 1992 Bounds, Quadratic Differentials, and Renormalization Conjectures (Providence, RI: American Mathematical Society)