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Mane, R.; Sad, P.; Sullivan, D.

On the dynamics of rational maps. (English) Zbl 0524.58025

Ann. Sci. Éc. Norm. Supér. (4) 16, 193-217 (1983).
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Cited in 20 Reviews
Cited in 260 Documents

MSC:

37A99 Ergodic theory
54H20 Topological dynamics (MSC2010)
30C62 Quasiconformal mappings in the complex plane
28D20 Entropy and other invariants

Keywords:

holomorphic variation of rational maps; axiom A; Julia set; holomorphic family of continuous maps

Citations:

Zbl 0524.58024
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Full Text: DOI Numdam EuDML

References:

[1] R. BOWEN , Hausdorff Dimension of Quasi Circles (Publications Mathematiques I.H.E.S., Vol. 50, 1979 , pp. 11-25). Numdam | MR 81g:57023 | Zbl 0439.30032 · Zbl 0439.30032 · doi:10.1007/BF02684767
[2] C. CAMACHO , On the Local Structure of Conformal Mappings and Holomorphic Vector Fields in C2 (Astérisque, Vol. 59-60, 1978 , pp. 83-94). MR 81d:58016 | Zbl 0415.30015 · Zbl 0415.30015
[3] M. FATOU , Sur les équations fonctionnelles (Bull. Soc. Math. Fr., Vol. 47, 1919 , pp. 161-271, Vol. 48, 1920 , pp. 33-94 and pp. 208-314). Numdam | JFM 47.0921.02 · JFM 47.0921.02
[4] S. LATTES , Sur l’itération des substitutions rationnelles et les fonctions de Poincaré (C.R. Acad. Sc., Paris, T. 166, 1918 , pp. 26-28). JFM 46.0522.01 · JFM 46.0522.01
[5] M. V. JACOBSON , On the Question of the Classification of Rational Maps of Riemann Sphere (Uspehi Mat. Nauk., Vol. 28, 1973 , pp. 247-248).
[6] G. JULIA , Sur l’itération des fonctions rationnelles (Journal de Math. Pure et Appliquée, Vol. 8, 1918 , pp. 47-245). Article | JFM 46.0520.06 · JFM 46.0520.06
[7] D. RUELLE , Analytic Repellors, Ergodic Theory and Dynamical Systems (to appear).
[8] C. L. SIEGEL , Iteration of Analytic Functions (Annals of Mathematics, Vol. 43, 1942 , pp. 607-612). MR 4,76c | Zbl 0061.14904 · Zbl 0061.14904 · doi:10.2307/1968952
[9] D. SULLIVAN , Quasi Conformal Homeomorphisms and Dynamics II (to appear).
[10] D. SULLIVAN , Conformal Dynamical Systems [Proc. of the International Symposium on Dynamical Systems, Rio de Janeiro, 1981 (to appear)].
[11] D. SULLIVAN , Density at Infinity (Publications Mathématiques I.H.E.S., Vol. 50, 1979 , pp. 419-450). Numdam | Zbl 0439.30034 · Zbl 0439.30034 · doi:10.1007/BF02684773
[12] D. SULLIVAN , Discrete Conformal Groups and Measurable Dynamics (Bull. of the A.M.S., Vol. 6, 1982 ). MR 83c:58066 | Zbl 0489.58027 · Zbl 0489.58027 · doi:10.1090/S0273-0979-1982-14966-7
[13] D. SULLIVAN , Quasi Conformal Homeomorphisms and Dynamics III (to appear).
[14] D. SULLIVAN and W. THURSTON , Extending Holomorphic Motions (to appear). · Zbl 0619.30026
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