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Hausdorff dimension in graph directed constructions

- R. Mauldin, S. C. Williams
- Mathematics
- 1 February 1988

We introduce the notion of geometric constructions in Rm governed by a directed graph G and by similarity ratios which are labelled with the edges of this graph. For each such construction, we… Expand

Dimensions and Measures in Infinite Iterated Function Systems

- R. Mauldin, M. Urbanski
- Mathematics
- 1 July 1996

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… Expand

Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets

- R. Mauldin, M. Urbanski
- Mathematics
- 18 August 2003

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.… Expand

Random recursive constructions: asymptotic geometric and topological properties

- R. Mauldin, S. C. Williams
- Mathematics
- 1986

We study some notions of "random recursive constructions" in Euclidean m-space which lead almost surely to a particular type of topological object; e.g., Cantor set, Sierpiriski curve or Menger… Expand

Multifractal decompositions of Moran fractals

- R. Cawley, R. Mauldin
- Mathematics
- 1 April 1992

We present a rigorous construction and generalization of the multifractal decomposition for Moran fractals with infinite product measure. The generalization is specified by a system of nonnegative… Expand

Gibbs states on the symbolic space over an infinite alphabet

- R. Mauldin, M. Urbanski
- Mathematics
- 1 December 2001

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… Expand

On the Hausdorff dimension of some graphs

- R. Mauldin, S. C. Williams
- Mathematics
- 1 February 1986

Consider the functions Wb(x)= b-cn[1(bnX + On)--1(0n)] n=-oo where b > 1, 0 0 such that if b is large enough, then the Hausdorff dimension of the graph of Wb is bounded below by 2a (C/ ln b). We also… Expand

Conformal iterated function systems with applications to the geometry of continued fractions

- R. Mauldin, M. Urbanski
- Mathematics
- 21 July 1999

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… Expand

Zero Temperature Limits of Gibbs-Equilibrium States for Countable Alphabet Subshifts of Finite Type

- O. Jenkinson, R. Mauldin, M. Urbanski
- Mathematics
- 1 May 2005

Let ΣA be a finitely primitive subshift of finite type on a countable alphabet. For appropriate functions f:ΣA → IR, the family of Gibbs-equilibrium states (μtf)t⩾1 for the functions tf is shown to… Expand

Some additive properties of sets of real numbers

- P. Erdös, K. Kunen, R. Mauldin
- Mathematics
- 1981

Some problems concerning the additive properties of subsets of R are investigated. From a result of G. G . Lorentz in additive number theory, we show that if P is a nonempty perfect subset of R, then… Expand

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