Related papers: Multifractal analysis of random weak Gibbs measure…
We achieve the multifractal analysis of a class of complex valued statistically self-similar continuous functions. For we use multifractal formalisms associated with pointwise oscillation exponents of all orders. Our study exhibits new…
In this paper, we study the Hausdorff dimension of the generalized intrinsic level set with respect to the given ergodic meausre in a class of non-uniformly hyperbolic interval maps with finitely many branches.
In Koeller \cite{koerprops} the twelve variants of the Reifenberg properties known to be instrumental in the theory of minimal surfaces were classified with respect to various Hausdorff measure based measure theoretic properties. The…
We consider partially hyperbolic \( C^{1+} \) diffeomorphisms of compact Riemannian manifolds of arbitrary dimension which admit a partially hyperbolic tangent bundle decomposition \( E^s\oplus E^{cu} \). Assuming the existence of a set of…
We give a systematic account of iterated function systems (IFS) of weak contractions of different types (Browder, Rakotch, topological). We show that the existence of attractors and asymptotically stable invariant measures, and the validity…
For a large class of self-similar sets F in R^d analogues of the higher order mean curvatures of differentiable submanifolds are introduced, in particular, the fractal Gauss-type curvature. They are shown to be the densities of associated…
We describe the shrinking target problem for random iterated function systems which semi-conjugate to a random subshifts of finite type. We get the Hausdorff dimension of the set based on shrinking target problems with given targets. The…
The method of iterated conformal maps allows to study the harmonic measure of Diffusion Limited Aggregates with unprecedented accuracy. We employ this method to explore the multifractal properties of the measure, including the scaling of…
We examine both the dynamical and the multifractal properties at the chaos threshold of logistic maps with general nonlinearity $z>1$. First we determine analytically the sensitivity to initial conditions $\xi_{t}$. Then we consider a…
We establish Euclidean-type lower bounds for the codimension-1 Hausdorff measure of sets that separate points in doubling and linearly locally contractible metric manifolds. This gives a quantitative topological isoperimetric inequality in…
We propose to study multiple ergodic averages from multifractal analysis point of view. In some special cases in the symbolic dynamics, Hausdorff dimensions of the level sets of multiple ergodic average limit are determined by using Riesz…
Let $(X,f)$ be a dynamical system with the specification property and $\varphi$ be continuous functions. In this paper, we establish some conditional variational principles for the upper and lower Bowen/packing metric mean dimension with…
We consider highly heterogeneous random networks with symmetric interactions in the limit of high connectivity. A key feature of this system is that the spectral density of the corresponding ensemble exhibits a divergence within the bulk.…
The aim of this paper is to study the behavior of the multifractal Hewitt-Stromberg dimension functions under projections in Euclidean space. As an application, we study the multifractal analysis of the projections of a measure. In…
We study the thermodynamic formalism for generalized Gibbs measures, such as renormalization group transformations of Gibbs measures or joint measures of disordered spin systems. We first show existence of the relative entropy density and…
In the present work, some density estimations associated with vector-valued quasi-Ahlfors measures are developed within the mixed multifractal analysis framework. The principle idea based on the fact that being quasi-Ahlfors is sufficient…
We discuss the dependence of set-valued dynamical systems on parameters. Under mild assumptions which are often satisfied for random dynamical systems with bounded noise and control systems, we establish the fact that topological…
Consider a sequence of linear contractions $S_{j}(x)=\varrho x+d_{j}$ and probabilities $p_{j}>0$ with $\sum p_{j}=1$. We are interested in the self-similar measure $\mu =\sum p_{j}\mu \circ S_{j}^{-1}$, of finite type. In this paper we…
We study the Hausdorff dimension of Gibbs measures with infinite entropy with respect to maps of the interval with countably many branches. We show that under simple conditions, such measures are symbolic-exact dimensional, and provide an…
Mesoscopic fluctuations of the local density of states encode multifractal correlations in disorderedelectron systems. We study fluctuations of the local density of states in a superconducting state of weakly disordered films. We perform…