Conformal measures for rational functions revisited

Fundamenta Mathematicae

Volumn 157, Issue 2-3, 1998, Pages 161-173

  Denker, M ^a   Mauldin, R D ^c   Nitecki, Z ^b   Urbanski M ^c  

^a Inst fuer Mathematische Stochastik   (Germany)

^b TUFTS UNIVERSITY   (United States)

^c UNIVERSITY OF NORTH TEXAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032356948     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. J. Aaronson, M. Denker and M. Urbański, Ergodic theory for Markov fibred systems and parabolic rational maps, Trans. Amer. Math. Soc. 337 (1993), 495-548.
2. A. M. Blokh, J. C. Mayer and L. G. Oversteegen, Limit sets and conformal measures, preprint, 1998.
3. M. Denker, Z. Nitecki and M. Urbański, Conformal measures and S-unimodal maps, in: Dynamical Systems and Applications, World Sci. Ser. Appl. Anal. 4, World Sci., 1995, 169-212.
4. M. Denker and M. Urbański, Ergodic theory of equilibrium states for rational maps, Nonlinearity 4 (1991), 103-134.
5. _, _, On Sullivan's conformal measures for rational maps of the Riemann sphere, ibid. 4 (1991), 365-384.
6. _, _, On absolutely continuous invariant measures for expansive rational maps with rationally indifferent periodic points, Forum Math. 3 (1991), 561-579.
7. _, _, Geometric measures for parabolic rational maps, Ergodic Theory Dynam. Systems 12 (1992), 53-66.
8. M. Lyubich and Y. Minsky, Laminations in holomorphic dynamics, J. Differential Geom. 47 (1997), 17-94.
9. R. Mañé, On the Bernoulli property of rational maps, Ergodic Theory Dynam. Systems 5 (1985), 71-88.
10. R. D. Mauldin and M. Urbański, Dimensions and measures in infinite iterated function systems, Proc. London Math. Soc. 73 (1996), 105-154.
11. C. T. McMullen, Hausdorff dimension and conformal dynamics II: Geometrically finite rational maps, preprint, Stony Brook, 1997.
12. F. Przytycki, Lyapunov characteristic exponents are nonnegative, Proc. Amer. Math. Soc. 119 (1993), 309-317.
13. _, Iterations of holomorphic Collet-Eckmann maps: Conformal and invariant measures. Appendix: On non-renormalizable quadratic polynomials, Trans. Amer. Math. Soc. 350 (1998), 717-742.
14. F. Przytycki, On measure and Hausdorff dimension of Julia sets for holomorphic Collet-Eckmann maps, in: Dynamical Systems (Montevideo, 1995), Pitman Res. Notes Math. 362, Longman, 1996, 167-181.
15. _, Conical limit set and Poincaré exponent for iterations of rational functions, preprint, 1997
16. F. Przytycki and M. Urbański, Fractal sets in the plane - ergodic theory methods, to appear.
17. M. Shishikura, The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets, preprint, 1991.
18. M. Urbański, Rational functions with no recurrent critical points, Ergodic Theory Dynam. Systems 14 (1994), 391-414.
19. _, On some aspects of fractal dimensions in higher dimensional dynamics, preprint, 1995.
20. _, Geometry and ergodic theory of conformal nonrecurrent dynamics, Ergodic Theory Dynam. Systems 17 (1997), 1449-1476.