Add to ORKGLet μ be a Borel probability measure generated by a hyperbolic recurrent iterated function system defined on a nonempty compact subset of Rk. We study the Hausdorff and the packing dimensions, and the quantization dimensions of μ with respect to the geometric mean error. The results establish the connections with various dimensions of the measure μ and generalize many known results about local dimensions and quantization dimensions of measures
We compute, for a compact set $K\subset\mathbb R^d$, the value of the upper and of the lower $L^q$-d...
We employ the ergodic-theoretic machinery of scenery flows to address classical geometric measure-th...
AbstractIn this paper, we study the quantization dimension of a random self-similar measure μ suppor...
We show that the asymptotic behavior of the quantization error allows the definition of dimensions f...
The term quantization refers to the process of estimating a given probability by a discrete probabil...
AbstractLet {fi}1N be a family of similitudes on R1 satisfying the strong separation condition and ν...
We provide a full picture of the upper quantization dimension in term of the R\'enyi dimension, in t...
AbstractLet μ be a Borel probability measure on Rd with compact support and D¯r(μ) the upper quantiz...
Various tools can be used to calculate or estimate the dimension of measures. Using a probabilistic ...
AbstractIn this paper we consider the Gibbs measure on the one-sided shift dynamical system and dete...
AbstractWe introduce a notion of monotonicity of dimensions of measures. We show that the upper and ...
AbstractThe quantization dimension function for a probability measure induced by a set of infinite c...
We investigate quantization coefficients for probability measures μ on limit sets, which are generat...
We prove the long-standing Eckmann-Ruelle conjecture in dimension theory of smooth dynamical systems...
openIn this thesis we introduce the concepts of Hausdorff dimensions and box-counting (or Minkowski-...
We compute, for a compact set $K\subset\mathbb R^d$, the value of the upper and of the lower $L^q$-d...
We employ the ergodic-theoretic machinery of scenery flows to address classical geometric measure-th...
AbstractIn this paper, we study the quantization dimension of a random self-similar measure μ suppor...
We show that the asymptotic behavior of the quantization error allows the definition of dimensions f...
The term quantization refers to the process of estimating a given probability by a discrete probabil...
AbstractLet {fi}1N be a family of similitudes on R1 satisfying the strong separation condition and ν...
We provide a full picture of the upper quantization dimension in term of the R\'enyi dimension, in t...
AbstractLet μ be a Borel probability measure on Rd with compact support and D¯r(μ) the upper quantiz...
Various tools can be used to calculate or estimate the dimension of measures. Using a probabilistic ...
AbstractIn this paper we consider the Gibbs measure on the one-sided shift dynamical system and dete...
AbstractWe introduce a notion of monotonicity of dimensions of measures. We show that the upper and ...
AbstractThe quantization dimension function for a probability measure induced by a set of infinite c...
We investigate quantization coefficients for probability measures μ on limit sets, which are generat...
We prove the long-standing Eckmann-Ruelle conjecture in dimension theory of smooth dynamical systems...
openIn this thesis we introduce the concepts of Hausdorff dimensions and box-counting (or Minkowski-...
We compute, for a compact set $K\subset\mathbb R^d$, the value of the upper and of the lower $L^q$-d...
We employ the ergodic-theoretic machinery of scenery flows to address classical geometric measure-th...
AbstractIn this paper, we study the quantization dimension of a random self-similar measure μ suppor...