Uniformly perfect sets, rational semigroups, kleinian groups and IFS's

Proceedings of the American Mathematical Society

Volumn 128, Issue 9, 2000, Pages 2569-2575

  Stankewitz, Rich ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Iterated function systems; Julia sets; Kleinian groups; Rational semigroups; Uniformly perfect

Indexed keywords

EID: 23044521705     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-00-05313-2     Document Type: Article

References (22)

1. I. N. Baker. Repulsive fixed points of entire functions. Math. Z., 104:252-256, 1968. MR 37:1599
2. A. F. Beardon and Ch. Pommerenke. The Poincarẽ metric of plane domains. J. London Math. Soc., 18:475-483, 1978. MR 80a:30020
3. Alan F. Beardon. The geometry of discrete groups. Springer-Verlag, New York, 1983. MR 85d:22026
4. Alan F. Beardon. Iterations of Rational Functions. Springer-Verlag, New York, 1991. MR 92j:30026
5. David Boyd. An invariant measure for finitely generated rational semigroups. Complex Variables, to appear.
6. Lennart Carleson and Theodore W. Gamelin. Complex Dynamics. Springer-Verlag, New York, 1993. MR 94h:30033
7. A. Eremenko. Julia sets are uniformly perfect. Preprint, Purdue University, 1992.
8. Kenneth Falconer. Fractal Geometry, Mathematical foundations and Applications. John Wiley and Sons, 1990. MR 92j:28008
9. A. Hinkkanen. Julia sets of rational functions are uniformly perfect. Math. Proc. Camb, Phil., 113:543-559, 1993. MR 94b:58084
10. A. Hinkkanen and G.J. Martin. The dynamics of semigroups of rational functions I. Proc. London Math. Soc.(3), 73:358-384, 1996. MR 97e:58198
11. A. Hinkkanen and G.J. Martin. Julia sets of rational semigroups. Math. Z., 222(2):161-169, 1996. MR 98d:30038
12. John E. Hutchinson. Fractals and self similarity. Indiana University Math. Journal, 30:731-747, 1981. MR 82h:49026
13. R. Mañé and L. F. da Rocha. Julia sets are uniformly perfect. Proc. Amer. Math. Soc., 116:251-257, 1992. MR 92k:58229
14. Ch. Pommerenke. Uniformly perfect sets and the poincare metric. Arch. Math., 32:192-199, 1979. MR 80j:30073
15. Ch. Pommerenke. On uniformly perfect sets and Fuchsian groups. Analysis, 4:299-321, 1984. MR 86e:30044
16. Fu-Yao Ren. Advances and problems in random dynamical systems. Preprint, 1998.
17. Wilhelm Schwick. Repelling periodic points in the Julia set. Bull. London Math. Soc., 29:314-316, 1997. MR 97m:30029
18. Rich Stankewitz. Completely invariant sets of normality for rational semigroups. Complex Variables. to appear.
19. Rich Stankewitz. Completely invariant Julia sets of rational semigroups. PhD thesis, University of Illinois, 1998.
20. Rich Stankewitz. Completely invariant Julia sets of polynomial semigroups. Proc. Amer. Math. Soc., 127:2889-2898, 1999. CMP 98:07
21. Hiroki Sumi. On hausdorff dimension of Julia sets of hyperbolic rational semigroups. Kodai Math. J., 21:10-28, 1998. CMP 98:12
22. Hiroki Sumi. On dynamics of hyperbolic rational semigroups. Journal of Mathematics of Kyoto University, to appear.