相关论文: A multifractal formalism for Hewitt-Stromberg meas…
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…
We introduce a mixed generalized multifractal formalism which extends the mixed multifractal formalism introduced by L. Olsen based on generalizations of the Hausdorff and packing measures. The validity of such a formalism is proved in some…
The multifractal formalism for measures hold whenever the existence of corresponding Gibbs-like measures supported on the singularities sets holds. In the present work we tried to relax such a hypothesis and introduce a more general…
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…
In this paper, we construct new multifractal measures, on the Euclidean space $\mathbb{R}^n$, in a similar manner to Hewitt-Stomberg measures but using the class of all $n$-dimensional half-open binary cubes of covering sets in the…
In this work, we investigate the H\"older spectrum of typical measures (in the Baire category sense) in a general compact set and we compute the multifractal spectrum of a typical measures supported by a self-similar set. Such mesures…
The multifractal formalism for measures in its original formulation is checked for special classes of measures such as doubling, self-similar, and Gibbs-like ones. Out of these classes, suitable conditions should be taken into account to…
We refine the multifractal formalism for the local dimension of a Gibbs measure $\mu$ supported on the attractor $\Lambda$ of a conformal iterated functions system on the real line. Namely, for given $\alpha\in \mathbb{R}$, we establish the…
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 consider the multifractal formalism for the dynamics of semigroups of rational maps on the Riemann sphere and random complex dynamical systems. We elaborate a multifractal analysis of level sets given by quotients of Birkhoff sums with…
In a previous work \cite{She} we constructed measures on symbolic spaces which satisfy an extended multifractal formalism (in the sense that Olsen's functions $b$ and $B$ differ and that their Legendre transforms have the expected…
For a positive measure set of nonuniformly expanding quadratic maps on the interval we effect a multifractal formalism, i.e., decompose the phase space into level sets of time averages of a given observable and consider the associated {\it…
Multifractal formalism is designed to describe the distribution at small scales of the elements of $\mathcal M^+_c(\R^d)$, the set of positive, finite and compactly supported Borel measures on $\R^d$. It is valid for such a measure $\mu$…
Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within…
In this paper, we study the multifractal Hausdorff and packing dimensions of Borel probability measures and study their behaviors under orthogonal projections. In particular, we try through these results to improve the main result of M. Dai…
We propose to study the multifractal behavior of weighted ergodic averages. Our study in this paper is concentrated on the symbolic dynamics. We introduce a thermodynamical formalism which leads to a multifractal spectrum. It is proved that…
It has often been observed that the Multifractal Formalism and the Large Deviation Principles are intimately related. In fact, Multifractal Formalism was heuristically derived using the Large Deviations ideas. In numerous examples in which…
We present a multifractal formalism for measures on infinite dimensional metric spaces, in terms of scales instead of dimensions in the classical multifractal analysis. We prove a multifractal formalism with a suitable scaling, called…
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 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…