Displaying similar documents to “On the Hyperbolic Hausdorff Dimension of the Boundary of a Basin of Attraction for a Holomorphic Map and of Quasirepellers”

Expanding repellers in limit sets for iterations of holomorphic functions

Feliks Przytycki (2005)

Fundamenta Mathematicae

Similarity:

We prove that for Ω being an immediate basin of attraction to an attracting fixed point for a rational mapping of the Riemann sphere, and for an ergodic invariant measure μ on the boundary FrΩ, with positive Lyapunov exponent, there is an invariant subset of FrΩ which is an expanding repeller of Hausdorff dimension arbitrarily close to the Hausdorff dimension of μ. We also prove generalizations and a geometric coding tree abstract version. The paper is a continuation of a paper in Fund....

On the Hausdorff dimension of piecewise hyperbolic attractors

Tomas Persson (2010)

Fundamenta Mathematicae

Similarity:

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.

Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials

Apostolova, Lilia N. (2012)

Mathematica Balkanica New Series

Similarity:

MSC 2010: 30C10, 32A30, 30G35 The algebra R(1; j; j2; j3), j4 = ¡1 of the fourth-R numbers, or in other words the algebra of the double-complex numbers C(1; j) and the corresponding functions, were studied in the papers of S. Dimiev and al. (see [1], [2], [3], [4]). The hyperbolic fourth-R numbers form other similar to C(1; j) algebra with zero divisors. In this note the square roots of hyperbolic fourth-R numbers and hyperbolic complex numbers are found. The quadratic equation...

Levi-flat filling of real two-spheres in symplectic manifolds (II)

Hervé Gaussier, Alexandre Sukhov (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

We consider a compact almost complex manifold ( M , J , ω ) with smooth Levi convex boundary ∂ M and a symplectic tame form ω . Suppose that S 2 is a real two-sphere, containing complex elliptic and hyperbolic points and generically embedded into ∂ M . We prove a result on filling S 2 by holomorphic discs.

Topological Pressure for One-Dimensional Holomorphic Dynamical Systems

Katrin Gelfert, Christian Wolf (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

For a class of one-dimensional holomorphic maps f of the Riemann sphere we prove that for a wide class of potentials φ the topological pressure is entirely determined by the values of φ on the repelling periodic points of f. This is a version of a classical result of Bowen for hyperbolic diffeomorphisms in the holomorphic non-uniformly hyperbolic setting.

Remarks on the relative intrinsic pseudo-distance and hyperbolic imbeddability

Nguyen Doan Tuan, Pham Viet Duc (2005)

Annales Polonici Mathematici

Similarity:

We prove the invariance of hyperbolic imbeddability under holomorphic fiber bundles with compact hyperbolic fibers. Moreover, we show an example concerning the relation between the Kobayashi relative intrinsic pseudo-distance of a holomorphic fiber bundle and the one in its base.

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

Huaibin Li, Weixiao Shen (2008)

Fundamenta Mathematicae

Similarity:

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.

Combinatorial Modulus on Boundary of Right-Angled Hyperbolic Buildings

Antoine Clais (2016)

Analysis and Geometry in Metric Spaces

Similarity:

In this article, we discuss the quasiconformal structure of boundaries of right-angled hyperbolic buildings using combinatorial tools. In particular, we exhibit some examples of buildings of dimension 3 and 4 whose boundaries satisfy the combinatorial Loewner property. This property is a weak version of the Loewner property. This is motivated by the fact that the quasiconformal structure of the boundary led to many results of rigidity in hyperbolic spaces since G.D.Mostow. In the case...