Parabolic Cantor sets
Fundamenta Mathematicae (1996)
- Volume: 151, Issue: 3, page 241-277
- ISSN: 0016-2736
Access Full Article
topAbstract
topHow to cite
topReferences
top- [ADU] J. Aaronson, M. Denker, and M. Urbański, Ergodic theory for Markov fibered systems and parabolic rational maps, Trans. Amer. Math. Soc. 337 (1993), 495-548. Zbl0789.28010
- [Be] T. Bedford, Applications of dynamical systems theory to fractals - a study of cookie-cutter Cantor sets, preprint, 1989.
- [Bo] R. Bowen, Equilibrium States and the Ergodic Theory for Anosov Diffeomorphisms, Lecture Notes in Math. 470, Springer, 1975. Zbl0308.28010
- [DU1] M. Denker and M. Urbański, Hausdorff and conformal measures on Julia sets with a rationally indifferent periodic point, J. London Math. Soc. 43 (1991), 107-118. Zbl0734.28007
- [DU2] M. Denker and M. Urbański, On absolutely continuous invariant measures for expansive rational maps with rationally indifferent periodic points, Forum Math. 3 (1991), 561-579. Zbl0745.28008
- [DU3] M. Denker and M. Urbański, Geometric measures for parabolic rational maps, Ergodic Theory Dynam. Systems 12 (1992), 53-66. Zbl0737.58030
- [DU4] M. Denker and M. Urbański, The capacity of parabolic Julia sets, Math. Z. 211 (1992), 73-86. Zbl0763.30009
- [DU5] M. Denker and M. Urbański, On Sullivan's conformal measures for rational maps of the Riemann sphere, Nonlinearity 4 (1991), 365-384. Zbl0722.58028
- [DU6] M. Denker and M. Urbański, On the existence of conformal measures, Trans. Amer. Math. Soc. 328 (1991), 563-587. Zbl0745.58031
- [LS] R. de la Llave and R. P. Schafer, Rigidity properties of one dimensional expanding maps, preprint, 1994.
- [Ma] P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press, 1995. Zbl0819.28004
- [Po] C. Pommerenke, Boundary Behaviour of Conformal Maps, Springer, Berlin, 1992. Zbl0762.30001
- [Pr1] F. Przytycki, Iterations of holomorphic Collet-Eckmann maps: conformal and invariant measures, preprint, 1995.
- [Pr2] F. Przytycki, Cantor repellers in the line, scaling functions, an application to Feigenbaum’s universality, preprint, 1991.
- [Pr3] F. Przytycki, Sullivan's classification of conformal expanding repellers, preprint, 1991.
- [Pr4] F. Przytycki, On holomorphic perturbations of , Bull. Polish Acad. Sci. Math. 34 (1986), 127-132.
- [PT] F. Przytycki and F. Tangerman, Cantor sets in the line: Scaling functions of the shift map, preprint, 1992.
- [PU] F. Przytycki and M. Urbański, Fractals in the complex plane - ergodic theory methods, to appear. Zbl1202.37001
- [PUZ] F. Przytycki, M. Urbański, and A. Zdunik, Harmonic, Gibbs and Hausdorff measures on repellers for holomorphic maps II, Studia Math. 97 (1991), 189-225. Zbl0732.58022
- [Ru] D. Ruelle, Thermodynamic Formalism, Addison-Wesley, 1978.
- [Sc] F. Schweiger, Number theoretical endomorphisms with σ-finite invariant measures, Israel J. Math. 21, (1975), 308-318.
- [SS] M. Shub and D. Sullivan, Expanding endomorphisms of the circle revisited, Ergodic Theory Dynam. Systems, 5 (1985), 285-289. Zbl0583.58022
- [Su1] D. Sullivan, Quasiconformal homeomorphisms in dynamics, topology, and geometry, in: Proc. Internat. Congress of Math., Berkeley, Amer. Math. Soc., 1986, 1216-1228.
- [Su2] D. Sullivan, Differentiable structures on fractal-like sets, determined by intrinsic scaling functions on dual Cantor sets, in: The Mathematical Heritage of Herman Weyl, Proc. Sympos. Pure Math. 48, Amer. Math. Soc., 1988, 15-23.
- [TT] S. J. Taylor and C. Tricot, Packing measure, and its evaluation for a Brownian path, Trans. Amer. Math. Soc. 288 (1985), 679-699. Zbl0537.28003
- [U1] M. Urbański, On the Hausdorff dimension of a Julia set with a rationally indifferent periodic point, Studia Math. 97 (1991), 167-188. Zbl0727.58024
- [U2] M. Urbański, Rational functions with no recurrent critical points, Ergodic Theory Dynam. Systems 14 (1994), 391-414. Zbl0807.58025
- [Wa] P. Walters, A variational principle for the pressure of continuous transformations, Amer. J. Math. 97 (1975), 937-971. Zbl0318.28007