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Hölder implies Collet-Eckmann. (English) Zbl 0939.37026
Flexor, Marguerite (ed.) et al., Géométrie complexe et systèmes dynamiques. Colloque en l’honneur d’Adrien Douady à l’occasion du soixantième anniversaire, Orsay, France, du 3 au 8 juillet 1995. Paris: Astérisque, Astérisque. 261, 385-403 (2000).
Summary: The author proves that for every polynomial $$f$$ if its basin of attraction to $$\infty$$ is Hölder and the Julia set contains only one critical point $$c$$ then $$f$$ is Collet-Eckmann, namely there exists $$\lambda>1$$, $$C>0$$ such that, for every $$n\geq 0$$, $$|(f^n)'(f(c))|\geq C\lambda^n$$. He introduces also topological Collet-Eckmann rational maps and repellers.
For the entire collection see [Zbl 0932.00046].

##### MSC:
 37F50 Small divisors, rotation domains and linearization in holomorphic dynamics 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 37L45 Hyperbolicity; Lyapunov functions for infinite-dimensional dissipative dynamical systems