On the hyperbolicity of the period-doubling fixed point

Transactions of the American Mathematical Society

Volumn 358, Issue 4, 2006, Pages 1827-1846

  Smania, Daniel ^a,b  

^a UNIVERSITY OF TORONTO   (Canada)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Holomorphic motion, feigenbaum; Hyperbolicity; Parabolic domain, petals; Period doubling; Renormalization; Semi attractive; Universality

Indexed keywords

EID: 33645764339     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-05-03803-1     Document Type: Article

References (17)

1. [AB] L. Ahlfors and L. Bers. Riemann's mapping theorem for variable metrics. Ann. of Math., 72:385-404, 1960. MR0115006 (22:5813)
2. [ALdM] A. Avila, M. Lyubich and W. de Melo. Regular or stochastic dynamics in real analytic families of unimodal maps. Invent. Math. 154:451-550, 2003. MR2018784
3. [DH] A. Douady and J. Hubbard. On the dynamics of polynomial-like mappings. Ann. Sci. École Norm. Sup (4), 18:287-343, 1985. MR0816367 (87f:58083)
4. p. Publ. Mat. 38, 479-499, 1994. MR1316642 (96a:32050)
5. [Lan] O. Lanford. A computer-assisted proof of the Feigenbaum conjectures. Bull. Amer. Math. Soc. 6:427-434, 1982. MR0648529 (83g:58051)
6. [Lyu97] M. Lyubich. Dynamics of quadratic polynomials, I-II. Acta Math., 178:185-297, 1997. MR1459261 (98e:58145)
7. [Lyu99] M. Lyubich. Feigenbaum-Coullet-Tresser universality and Milnor's hairness conjecture. Ann. of Math., 149:319-420, 1999. MR1689333 (2000d:37051)
8. [Lyu02] M. Lyubich. Almost every real quadratic map is either regular or stochastic. Ann. of Math., 156:1-78, 2002. MR1935840 (2003i:37032)
9. [McM94] C. McMullen. Complex dynamics and renormalization. Annals of Mathematics Studies, 135, Princeton University Press, Princenton, 1994. MR1312365 (96b:58097)
10. [McM96] C. McMullen. Renormalization and 3-manifolds which fiber over the circle. Annals of Mathematics Studies, 142, Princeton University Press, Princenton, 1996. MR1401347 (97f:57022)
11. [M] R. Mañé. Lyapounov exponents and stable manifolds for compact transformations, in Geometric dynamics (Rio de Janeiro, 1981), Lectures Notes in Math. 1007, 522-577. MR0730286 (85j:58126)
12. [MSS] R. Mañé; P. Sad and D. Sullivan. On the dynamics of rational maps. Ann. Sci. Ecole Norm. Sup., 16:193-217, 1983. MR0732343 (85j:58089)
13. [Sm01] D. Smania. Renormalization theory for multimodal maps. Eletronic Preprint, IMPA, 2001. Available at www.icmc.usp.br/~smania/.
14. [Sm02a] D. Smania. Puzzle geometry and rigidity: The Fibonacci cycle is hyperbolic. Eletronic Preprint, 2002. Available at www.icmc.usp.br/~smania/.
15. [Sm03] D. Smania. On Feigenbaum eigenvectors. In preparation, 2003.
16. [Su] D. Sullivan. Bounds, quadratic differentials and renormalization conjectures, in American Mathematical Society Centennial publications: Vol. II (Providence, RI, 1988, 417-466,
17. Amer. Math. Soc. Providence, 1992. MR1184622 (93k:58194)