Displaying similar documents to “Absolutely Continuous Invariant Measures for Expansive Rational Maps with Rationally Indifferent Periodic Points.”

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.

Conformal measures for rational functions revisited

Manfred Denker, R. Mauldin, Z. Nitecki, Mariusz Urbański (1998)

Fundamenta Mathematicae

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We show that the set of conical points of a rational function of the Riemann sphere supports at most one conformal measure. We then study the problem of existence of such measures and their ergodic properties by constructing Markov partitions on increasing subsets of sets of conical points and by applying ideas of the thermodynamic formalism.

Intertwined internal rays in Julia sets of rational maps

Robert L. Devaney (2009)

Fundamenta Mathematicae

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We show how the well-known concept of external rays in polynomial dynamics may be extended throughout the Julia set of certain rational maps. These new types of rays, which we call internal rays, meet the Julia set in a Cantor set of points, and each of these rays crosses infinitely many other internal rays at many points. We then use this construction to show that there are infinitely many disjoint copies of the Mandelbrot set in the parameter planes for these maps.

Program

(1990)

Annales de l'I.H.P. Physique théorique

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