Diophantine approximation for conformal measures of one-dimensional iterated function systems

Rigorous Approximation of Stationary Measures for Iterated Function Systems

We study the problem of the rigorous computation of the stationary measure of an IFS described by a stochastic mixture of two or more dynamical systems which are either all uniformly expanding on the interval, either all contractive. In the expanding case, the associated transfer operators satisfy a LasotaYorke inequality, and we compute rigorously the approximations in the L1 norm. The rigorou...

Rigidity of Multi - Dimensional Conformal Iterated Function

The paper starts with an appropriate version of the bounded distortion theorem. We show that for a regular, satisfying the "Open Set Condition", iterated function system of countably many conformal contractions of an open connected subset of a Euclidean space IR d with d 3, the Radon-Nikodym derivative dd=dm has a real-analytic extension on an open neighbourhood of the limit set of this system,...

Separation conditions for conformal iterated function systems

Weextend both theweak separation condition and the finite type condition to include finite iterated function systems (IFSs) of injective C1 conformal contractions on compact subsets of Rd . For conformal IFSs satisfying the bounded distortion property, we prove that the finite type condition implies the weak separation condition. By assuming the weak separation condition, we prove that the Haus...

Quantization Dimension for Conformal Iterated Function Systems

Rigidity of In nite one-dimensional Iterated Function Systems

In MU] there has been introduced and developed the concept of innnite conformal iterated function systems. In this paper we consider 1-dimensional systems. We provide necessary and suucient conditions for such systems to be bi-Lipschitz equivalent. We extend to such systems the concept of scaling functions and we pay special attention to the real-analytic systems.