On the dimension spectra of infinite conformal iterated function systems

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...

Quantization Dimension for Conformal Iterated Function Systems

The Doubling Property of Conformal Measures of Infinite Iterated Function Systems

Hausdorff Dimension of the Limit Set of Conformal Iterated Function Systems with Overlaps

We give a new approach to the study of conformal iterated function systems with arbitrary overlaps. We provide lower and upper estimates for the Hausdorff dimension of the limit sets of such systems; these are expressed in terms of the topological pressure and the function d, counting overlaps. In the case when the function d is constant, we get an exact formula for the Hausdorff dimension. We ...

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...