Porosity of Julia sets of non-recurrent and parabolic Collet-Eckmann rational functions

Annales Academiae Scientiarum Fennicae Mathematica

Volumn 26, Issue 1, 2001, Pages 125-154

  Przytycki, F ^a   Urbanski M ^b  

^a INSTITUTE OF MATHEMATICS   (Poland)

^b UNIVERSITY OF NORTH TEXAS   (United States)

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[No Author keywords available]

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EID: 20644439768     PISSN: 1239629X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. [ADU] AARONSON, J., M. DENKER, and M. URBAŃSKI: Ergodic theory for Markov fibred systems and parabolic rational maps. - Trans. Amer. Math. Soc. 337, 1993, 495-548.
2. [CE1] COLLET, P., and J.-P. ECKMANN: On the abundance of aperiodic behaviour for maps on the interval. - Comm. Math. Phys. 73, 1980, 115-160.
3. [CE2] COLLET, P., and J.-P. ECKMANN: Positive Lyapunov exponents and absolute continuity for maps of the interval. - Ergodic Theory Dynam. Systems 3, 1983, 13-46.
4. [CJY] CARLESON, L., P. JONES, and J.-C. YOCCOZ: Julia and John. - Bol. Soc. Brasil. Mat. 25, 1994, 1-30.
5. [DH DOUADY, A., and J.H. HUBBARD: Etude dynamique des polynomes complexes (Deuxième partie). - Publ. Math. Orsay 85.4.
6. [DPU] DENKER, M., F. PRZYTYCKI, and M. URBAŃSKI: On the transfer operator for rational functions on the Riemann sphere. - Ergodic Theory Dynam. Systems 16:2, 1996, 255-266.
7. [DU] DENKER, M., and M. URBAŃSKI: The capacity of parabolic Julia sets. - Math. Z. 211, 1992, 73-86.
8. [Ge] GEYER, L.: Porosity of parabolic Julia sets. - Complex Variables Theory Appl. 39:3, 1999, 191-198.
9. [GS1] GRACZYK, J., and S. SMIRNOV: Collet, Eckmann and Hölder. - Invent. Math. 133:1, 1998, 69-96.
10. [GS2] GRACZYK, J., and S. SMIRNOV: Weak expansion and geometry of the Julia sets.- Preprint, 1997.
11. [KR] KOSKELA, P., and S. ROHDE: Hausdorff dimension and mean porosity. - Math. Ann. 309, 1997, 593-609.
12. [Le] LEVIN, G.: On backward stability of holomorphic dynamical systems. - Fund. Math. 158:2, 1998, 97-107.
13. [Ma] MAÑÉ, R.: On a theorem of Fatou. - Bol. Soc. Brasil. Mat. 24, 1993, 1-12.
14. [MCM] McMULLEN, C.: Self-similarity of Siegel disks and Hausdorff dimension of Julia sets. - Acta Math. 180:2, 1998, 247-292.
15. [NP] NOWICKI, T., and F. PRZYTYCKI: Topological invariance of the Collet-Eckmann property for S-unimodal maps. - Fund. Math. 155, 1998, 33-43.
16. [P1] PRZYTYCKI, F.: Iterations of holomorphic Collet-Eckmann maps: conformal and invariant measures. - Trans. Amer. Math. Soc. 350:2, 1998, 717-742.
17. [P2] PRZYTYCKI, F.: On measure and Hausdorff dimension of Julia sets for holomorphic Collet-Eckmann maps. - In: The Proceedings of the International Conference on Dynamical Systems, Montevideo 1995. Pitman Res. Notes Math. Ser. 362, 1996, 167-181.
18. [P3] PRZYTYCKI, F.: Hölder implies Collet-Eckmann. - Astérisque 261, Géométrie Complexe et Systèmes Dynamiques, Colloque en l'Honneur d'Adrien Douady, Orsay 1995, 2000, 385-403.
19. [PRS] PRZYTYCKI, F., J. RIVERA-LETELIER, and S. SMIRNOV: Relations between Collet-Eckmann type properties for iterations of rational functions. - In preparation.
20. [PR1] PRZYTYCKI, F., and S. ROHDE: Porosity of Collet-Eckmann Julia sets. - Fund. Math. 155, 1998, 189-199.
21. [PR2] PRZYTYCKI, F., and S. ROHDE: Rigidity of holomorphic Collet-Eckmann repellers. - Ark. Mat. 37, 1999, 357-371.
22. [U1] URBAŃSKI, M.: Rational functions with no recurrent critical points. - Ergodic Theory Dynam. Systems 14, 1994, 391-414.
23. [U2] URBAŃSKI, M.: Geometry and ergodic theory of conformal nonrecurrent dynamics. - Ergodic Theory Dynam. Systems 17, 1997, 1449-1476.