Displaying similar documents to “Rigidity and inflexibility in conformal dynamics.”

Normal points for generic hyperbolic maps

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.

Inhomogeneities in non-hyperbolic one-dimensional invariant sets

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...

Dimensions of the Julia sets of rational maps with the backward contraction property

Huaibin Li, Weixiao Shen (2008)

Fundamenta Mathematicae

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Consider a rational map f on the Riemann sphere of degree at least 2 which has no parabolic periodic points. Assuming that f has Rivera-Letelier's backward contraction property with an arbitrarily large constant, we show that the upper box dimension of the Julia set J(f) is equal to its hyperbolic dimension, by investigating the properties of conformal measures on the Julia set.

On the Hausdorff dimension of piecewise hyperbolic attractors

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.

Perturbations of flexible Lattès maps

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.