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

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

Refined measurable rigidity and flexibility for conformal iterated function systems

In this paper we investigate aspects of rigidity and flexibility for conformal iterated function systems. For the case in which the systems are not essentially affine we show that two such systems are conformal equivalent if and only if in each of their Lyapunov spectra there exists at least one level set such that the corresponding Gibbs measures coincide. We then proceed by comparing this res...

Quantization Dimension for Infinite Conformal Iterated Function Systems

The quantization dimension function for an F -conformal measure mF generated by an infinite conformal iterated function system satisfying the strong open set condition and by a summable Hölder family of functions is expressed by a simple formula involving the temperature function of the system. The temperature function is commonly used to perform a multifractal analysis, in our context of the m...

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,...