The doubling property of conformal measures of infinite iterated function systems

The Doubling Property of Conformal Measures of Infinite 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...

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

Infinite Iterated Function

We examine iterated function systems consisting of a countably innnite number of contracting mappings (IIFS). We state results analogous to the well-known case of nitely many mappings (IFS). Moreover, we show that IIFS can be approximated by appropriately chosen IFS both in terms of Hausdorff distance and of Hausdorff dimension. Comparing the descriptive power of IFS and IIFS as mechanisms deen...