Topological invariance of the Collet-Eckmann property for S-unimodal maps

Fundamenta Mathematicae

Volumn 155, Issue 1, 1998, Pages 33-43

  Nowicki, Tomasz ^a   Przytycki, Feliks ^b  

^a UNIVERSITY OF WARSAW   (Poland)

^b INSTITUTE OF MATHEMATICS   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040163957     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. H. Bruin, Invariant measures of interval maps, PhD thesis, Tech. Univ. Delft, 1994.
2. _, Topological conditions for the existence of invariant measures for unimodal maps, Ergodic Theory Dynam. Systems 14 (1994), 433-452.
3. P. Collet and J.-P. Eckmann, Positive Lyapunov exponents and absolute continuity for maps of the interval, ibid. 3 (1983), 13-46.
4. L. Carleson, P. Jones and J.-C. Yoccoz, Julia and John, Bol. Soc. Brasil. Mat. 25 (1994), 1-30.
5. M. Denker, F. Przytycki and M. Urbański, On the transfer operator for rational functions on the Riemann sphere, Ergodic Theory Dynam. Systems 16 (1996), 255-266.
6. J. Graczyk and S. Smirnov, Collet, Eckmann, & Hölder, Invent. Math., to appear.
7. M. Jakobson and G. Świ̧tek, Metric properties of non-renormalizable S-unimodal maps, II. Quasisymmetric conjugacy classes, Ergodic Theory Dynam. Systems 15 (1995), 871-938.
8. R. Mañé, On a theorem of Fatou, Bol. Soc. Brasil. Mat. 24 (1993), 1-12.
9. W. de Melo and S. van Strien, One-Dimensional Dynamics, Springer, 1993.
10. T. Nowicki and F. Przytycki, The conjugacy of Collet-Eckmann's map of the interval with the tent map is Hölder continuous, Ergodic Theory Dynam. Systems 9 (1989), 379-388.
11. T. Nowicki and D. Sands, Nonuniform hyperbolicity and universal bounds for S-unimodal maps, Invent. Math., to appear.
12. F. Przytycki, Iterations of holomorphic Collet-Eckmann maps, conformal and invariant measures, Trans. Amer. Math. Soc., to appear.
13. _, On measure and Hausdorff dimension of Julia sets for holomorphic Collet-Eckmann maps, in: International Conference on Dynamical Systems, Montevideo 1995 - a Tribute to Ricardo Mañé (F. Ledrappier, J. Lewowicz and S. Newhouse, eds.), Pitman Res. Notes Math. Ser. 362, Longman, 1996, 167-181.
14. _, Lyapunov characteristic exponents are nonnegative, Proc. Amer. Math. Soc. 119 (1993), 309-317.
15. _, Hölder implies CE, Astérisque, volume dedicated to A. Douady on his 60th birthday, to appear.
16. F. Przytycki and S. Rohde, Porosity of Collet-Eckmann Julia sets, Fund. Math., to appear.
17. _, _, Rigidity of holomorphic Collet-Eckmann repellers, preprint, May 1997.
18. D. Sands, Topological conditions for positive Lyapunov exponent in unimodal case, Ph.D. thesis, St. John's College, Cambridge, 1995.
19. D. Sands and T. Nowicki, Quasisymmetric conjugacies of Collet-Eckmann maps, Ergodic Theory Dynam. Systems, to appear.