Multifractal Analysis for Parabolically Semihyperbolic Generalized Polynomial-like Maps

Real Analyticity of Topological Pressure for Parabolically Semihyperbolic Generalized Polynomial-like Maps

Analytic Families of Semihyperbolic Generalized Polynomial-like Mappings

We show that the Hausdorff dimension of Julia sets in any analytic family of semihyperbolic generalized polynomial-like mappings (GPL) depends in a real-analytic manner on the parameter. For the proof we introduce abstract weakly regular analytic families of conformal graph directed Markov systems. We show that the Hausdorff dimension of limit sets in such families is real-analytic, and we asso...

Singularities of Schröder Maps and Unhyperbolicity of Rational Functions

We study transcendental singularities of a Schröder map arising from a rational function f , using results from complex dynamics and Nevanlinna theory. These maps are transcendental meromorphic functions of finite order in the complex plane. We show that their transcendental singularities lie over the set where f is not semihyperbolic (unhyperbolic). In addition, if they are direct, then they l...

Prediction uncertainty for tracer migration in random heterogeneities with multifractal character

Travel-time statistics for non-reacting tracers in fractal and multifractal media are addressed through numerical simulations. The logarithm of hydraulic conductivity is modeled using fractional Brownian motion (fBm) and more recently developed multifractal model based on bounded fractional Levy motion (bfLm). These models have been shown previously to accurately reproduce statistical propertie...

A Multifractal Analysis of Gibbs Measures for Conformal Expanding Maps and Markov Moran Geometric Constructions

We establish the complete multifractal formalism for Gibbs measures for confor-mal expanding maps and Markov Moran geometric constructions. Examples include Markov maps of an interval, hyperbolic Julia sets, and conformal toral endomorphisms. This paper describes the multifractal analysis of measures invariant under dynamical systems. The concept of a multifractal analysis was suggested by seve...