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The Hausdorff and packing measures and dimensions of the limit sets of iterated function systems generated by countable families of conformal contractions are investigated. Conformal measures for… (More)

Introduction 1. Symbolic dynamics 3. Holder families of functions 4. Conformal graph directed Markov systems 5. Examples of graph directed Markov systems 6. Conformal iterated function systems 7.… (More)

Introduction Basic examples and definitions 1. Measure preserving endomorphisms 2. Compact metric spaces 3. Distance expanding maps 4. Thermodynamical formalism 5. Expanding repellers in manifolds… (More)

We first use Nevanlinna theory to provide full thermodynamical formalism for a very general class of meromorphic functions of finite order. Finer stochastic properties of the Perron-Frobenius… (More)

We consider subshifts of finite type on the symbolic space generated by incidence matrices over a countably infinite alphabet. We extend the definition of topological pressure to this context and, as… (More)

A paraboIic rational map of the Riemann sphere admits a non-atomic h-conformal measure on its Julia set where h = the Hausdorff dimension of the Julia set and satisfies 1/2 < h < 2. With respect to… (More)

We develop the thermodynamic formalism for equilibrium states of strongly Hölder families of functions. These equilibrium states are supported on the limit set generated by iterating a system of… (More)

In this paper we obtain some results about general conformal iterated function systems. We obtain a simple characterization of the packing dimension of the limit set of such systems and introduce… (More)

In this paper we introduce and explore conformal parabolic iterated function systems. We deene and study topological pressure, Perron-Frobenius type operators, semi-conformal and conformal measures… (More)

We study the Hausdorff dimension of the intersection between stable manifolds and basic sets for an Axiom A holomorphic endomorphism on the complex projective space of dimension 2. We improve an… (More)