Quantization dimension function and Gibbs measure associated with Moran set

Quantization Dimension for Conformal Iterated Function Systems

Quantization dimension via quantization numbers

We give a characterization of the quantization dimension of Borel probability measures on R in terms of ε-quantization numbers. Using this concept, we show that the upper rate distortion dimension is not greater than the upper quantization dimension of order one. We also prove that the upper quantization dimension of a product measure is not greater than the sum of that of its marginals. Finall...

The Canonical Distortion Measure for Vector Quantization and Function Approximation

To measure the quality of a set of vector quantization points a means of measuring the distance between a random point and its quantization is required. Common metrics such as the Hamming and Euclidean metrics, while mathematically simple, are inappropriate for comparing natural signals such as speech or images. In this paper it is shown how an environment of functions on an input space X induc...

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...

Historic set carries full hausdorff dimension

‎We prove that the historic set for ratio‎ ‎of Birkhoff average is either empty or full of Hausdorff dimension in a class of one dimensional‎ ‎non-uniformly hyperbolic dynamical systems.