Related papers: Dimension spectrum for a nonconventional ergodic a…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
We compute the spectrum of anomalous dimensions of non-derivative composite operators with an arbitrary number of fields $n$ in the $O(N)$ vector model with cubic anisotropy at the one-loop order in the $\epsilon$-expansion. The complete…
This paper presents a simple method of calculating the Hausdorff dimension for a class of non-conformal fractals.
We consider measures which are invariant under a measurable iterated function system with positive, place-dependent probabilities in a separable metric space. We provide an upper bound of the Hausdorff dimension of such a measure if it is…
In the paper the general case of a normal discrete Hausdorff operators in $L^2(\mathbb{R}^d)$ is considered. The main result states that under some natural arithmetic condition the spectrum of such an operator is rotationally invariant.…
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…
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…
Given an $\alpha > 1$ and a $\theta$ with unbounded continued fraction entries, we characterise new relations between Sturmian subshifts with slope $\theta$ with respect to (i) an $\alpha$-H\"oder regularity condition of a spectral metric,…
We show some results about the Hausdorff dimension of particular minimal but not uniquely ergodic interval exchange transformations. There is an appendix which shows that typical points for two different ergodic measures of an interval…
In this paper, we show the following: the Hausdorff dimension of the spectrum of period-doubling Hamiltonian is bigger than $\log \alpha/\log 4$, where $\alpha$ is the Golden number; there exists a dense uncountable subset of the spectrum…
We compute the Hausdorff dimension of the image X(E) of a non random Borel set E $\subset$ [0, 1], where X is a L\'evy multistable process in R. This extends the case where X is a classical stable L\'evy process by letting the stability…
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…
Let $\{X_n= e^{2\pi i \theta_n}\}$ be a sequence of Steinhaus random variables, where $\theta_n$ are independent and uniformly distributed on $[0,1]$. We compute the almost sure Hausdorff dimension of the images and graphs of the random…
We show that the set of numbers that are $Q$-distribution normal but not simply $Q$-ratio normal has full Hausdorff dimension. It is further shown under some conditions that countable intersections of sets of this form still have full…
We analyse the dimension spectrum of continued fractions expansions with coefficients restricted to infinite subsets of $ \mathbb{N}$. We prove that the set of powers $P_q=\{q^n\colon n\in \mathbb{N}\}$ has full dimension spectrum for each…
Let $\nu_\lambda^p$ be the distribution of the random series $\sum_{n=1}^\infty i_n \lambda^n$, where $i_n$ is a sequence of i.i.d. random variables taking the values 0,1 with probabilities $p,1-p$. These measures are the well-known…
In this paper we study the dimension spectrum of continued fractions with coefficients restricted to infinite subsets of natural numbers. We prove that if $E$ is any arithmetic progression, the set of primes, or the set of squares…
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.
We consider expanding maps such that the unit interval can be represented as a full symbolic shift space with bounded distortion. There are already theorems about the Hausdorff dimension for sets defined by the set of accumulation points…
Exact Hausdorff dimensions are computed for singular continuous components of the spectral measures of a class of Schr\"odinger operators in bounded intervals.