Mark Pollicott (2009)
Fundamenta Mathematicae
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We consider families of hyperbolic maps and describe conditions for a fixed reference point to have its orbit evenly distributed for maps corresponding to generic parameter values.
Xavier Buff, Thomas Gauthier (2013)
Bulletin de la Société Mathématique de France
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We prove that any Lattès map can be approximated by strictly postcritically finite rational maps which are not Lattès maps.
Brian E. Raines (2004)
Fundamenta Mathematicae
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The topology of one-dimensional invariant sets (attractors) is of great interest. R. F. Williams [20] demonstrated that hyperbolic one-dimensional non-wandering sets can be represented as inverse limits of graphs with bonding maps that satisfy certain strong dynamical properties. These spaces have "homogeneous neighborhoods" in the sense that small open sets are homeomorphic to the product of a Cantor set and an arc. In this paper we examine inverse limits of graphs with more complicated...
M. Rees (1990)
Inventiones mathematicae
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Nicolae Mihalache (2011)
Fundamenta Mathematicae
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We show that the Fatou components of a semi-hyperbolic rational map are John domains. The converse does not hold. This compares to a famous result of Carleson, Jones and Yoccoz for polynomials, in which case the two conditions are equivalent. We show that a connected Julia set is locally connected for a large class of non-uniformly hyperbolic rational maps. This class is more general than semi-hyperbolicity and includes Collet-Eckmann maps, topological Collet-Eckmann...
Gallavotti, Giovanni (1998)
Documenta Mathematica
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Tomas Persson (2010)
Fundamenta Mathematicae
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We study non-invertible piecewise hyperbolic maps in the plane. The Hausdorff dimension of the attractor is calculated in terms of the Lyapunov exponents, provided that the map satisfies a transversality condition. Explicit examples of maps for which this condition holds are given.
F. Balibrea, C. La Paz (1997)
Annales Polonici Mathematici
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One-dimensional turbulent maps can be characterized via their ω-limit sets [1]. We give a direct proof of this characterization and get stronger results, which allows us to obtain some other results on ω-limit sets, which previously were difficult to prove.
Jerzy Dydak (1974)
Colloquium Mathematicae
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Gregory J. Davis (1990)
Publicacions Matemàtiques
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In this paper we provide a direct proof of hyperbolicity for a class of one-dimensional maps on the unit interval. The maps studied are degenerate forms of the standard quadratic map on the interval. These maps are important in understanding the Newhouse theory of infinitely many sinks due to homoclinic tangencies in two dimensions.
Andrzej Ehrenfeucht, Edward Grzegorek (1974)
Colloquium Mathematicae
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Cowen, Robert (2001)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Lluis Alsedà, Jaume Llibre (1989)
Banach Center Publications
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McMullen, Curtis T. (1998)
Documenta Mathematica
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Do Duc Thai (1991)
Annales Polonici Mathematici
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Abstract. The characterization of hyperbolic embeddability of relatively compact subspaces of a complex space in terms of extension of holomorphic maps from the punctured disc and of limit complex lines is given.
Kazimierz Włodarczyk (1993)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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A classical Julia-Carathéodory theorem concerning radial limits of holomorphic maps in one dimension is extended to hyperbolic contractions of bounded symmetric domains in J*-algebras.
N. Aoki, Kazumine Moriyasu, N. Sumi (2001)
Fundamenta Mathematicae
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We show that the C¹-interior of the set of maps satisfying the following conditions: (i) periodic points are hyperbolic, (ii) singular points belonging to the nonwandering set are sinks, coincides with the set of Axiom A maps having the no cycle property.