Related papers: A multifractal analysis for uniform level sets wit…
We introduce two frameworks in order to deal with fractal and multi-fractal analysis for subset sum problems where some embedding into the $1$-dimensional Euclidean space plays an important role. As one of these frameworks, the notion of…
We estimate the upper and lower bounds of the Hewitt$\textbf{-}$Stromberg dimensions. In particular, these results give new proofs of theorems on the multifractal formalism which is based on the Hewitt$\textbf{-}$Stromberg measures and…
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…
Dimensions of level sets of generic continuous functions and generic H\"older functions defined on a fractal $F$ encode information about the geometry, ``the thickness" of $F$. While in the continuous case this quantity is related to a…
Hausdorff dimension of level sets of generic continuous functions defined on fractals can give information about the "thickness/narrow cross-sections" "network" corresponding to a fractal set, $F$. This lead to the definition of the…
We study the set of irregular points for topologically mixing subshifts of finite type. It is well known that despite the irregular set having zero measure for every invariant measure, it has full topological entropy and full Hausdorff…
We establish uniform a-priori estimates for solutions of the semilinear Dirichlet problem \begin{equation} \begin{cases} (-\Delta)^m u=h(x,u)\quad&\mbox{in }\Omega,\\ u=\partial_nu=\cdots=\partial_n^{m-1}u=0\quad&\mbox{on }\partial\Omega,…
We describe the multifractal nature of random weak Gibbs measures on some class of attractors associated with $C^1$ random dynamics semi-conjugate to a random subshift of finite type. This includes the validity of the multifractal…
By an appropriate definition, we divide the irregular set into level sets. Then we characterize the multifractal spectrum of these new pieces by calculating their entropies. We also compute the entropies of various intersections of the…
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…
Incomplete U-statistics have been proposed to accelerate computation. They use only a subset of the subsamples required for kernel evaluations by complete U-statistics. This paper gives a finite sample bound in the style of Bernstein's…
In this article we prove estimates for the topological pressure of the set of points whose Birkhoff time averages are far from the space averages corresponding to the unique equilibrium state that has a weak Gibbs property. In particular,…
We introduce multifractal zeta-functions providing precise information of a very general class of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra of ergodic…
New proofs of theorems on the multifractal formalism are given. They yield results even at points q for which Olsen's functions b(q) and B(q) differ. Indeed, we provide an example of measure for which functions b and B differ and for which…
We provide a self-contained exposition of the well-known multifractal formalism for self-similar measures satisfying the strong separation condition. At the heart of our method lies a pair of quasiconvex optimization problems which encode…
We develop and analyze multilevel methods for nonuniformly elliptic operators whose ellipticity holds in a weighted Sobolev space with an $A_2$--Muckenhoupt weight. Using the so-called Xu-Zikatanov (XZ) identity, we derive a nearly uniform…
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
The dimension spectrum of a conformal iterated function system (CIFS) is the set of all Hausdorff dimensions of its various subsystem limit sets. This brief note provides two constructions -- (i) a compact perfect set that cannot be…
The aim of this paper is to study the multiplicity of solutions for the following Kirchhoff type elliptic systems \begin{eqnarray*} \left\{ \arraycolsep=1.5pt \begin{array}{ll} -m\left(\sum^k_{j=1}\|u_j\|^2\right)\Delta…