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Let $I=[0,1)$, $b\in \{2,3,\ldots\}$ and $f:I\to I$ be an injective piecewise $\frac{1}{b}$-affine map, that is, assume that there exists a partition of $I$ into intervals $I_1,\ldots,I_n$ such that $\vert f(x)-f(y)\vert\le\frac1b \vert…

The accumulation point of the period-tripling bifurcation cascade in complex quadratic map was discovered by Golberg, Sinai, and Khanin (Russ.Math.Surv. 38:1, 1983, 187), and independently by Cvitanovic and Myrheim (Phys.Lett. A94:8, 1983,…

By appropriate scaling of coupling constants a one-parameter family of ensembles of two-dimensional geometries is obtained, which interpolates between the ensembles of (generalized) causal dynamical triangulations and ordinary dynamical…

We expand a previous study [Phys. Rev. E 86, 051611 (2012)] on the conditions for occurrence of strong anisotropy (SA) in the scaling properties of two-dimensional surfaces displaying generic scale invariance. There, a natural Ansatz was…

We consider a family of CIFSs of the generalized complex continued fractions with a complex parameter space. We show that for each CIFS of the family, the Hausdorff measure of the limit set of the CIFS with respect to the Hausdorff…

Shrinking target problems in the context of iterated function systems have received an increasing amount of interest in the past few years. The classical shrinking target problem concerns points returning infinitely many times to a sequence…

We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…

We prove strong statistical stability of a large class of one-dimensional maps which may have an arbitrary finite number of discontinuities and of non-degenerate critical points and/or singular points with infinite derivative, and satisfy…

The form invariance of the statement of the maximum entropy principle and the metric structure in quantum density matrix theory, when generalized to nonextensive situations, is shown here to determine the structure of the nonextensive…

We derive, from conformal invariance and quantum gravity, the multifractal spectrum f(alpha,c) of the harmonic measure (or electrostatic potential, or diffusion field) near any conformally invariant fractal in two dimensions, corresponding…

Continuous-variable systems in quantum theory can be fully described through any one of the ${\rm s}$-ordered family of quasiprobabilities $\Lambda_{\rm s}(\alpha)$, ${\rm s} \in [-1,1]$. We ask for what values of $({\rm s}, a)$ is the…

Given an one-dimensional Lorenz-like expanding map we prove that the condition\linebreak $P_{top}(\phi,\partial \mathcal{P},\ell)<P_{top}(\phi,\ell)$ (see, subsection 2.4 for definition), introduced by Buzzi and Sarig in [1] is satisfied…

Let R be an o-minimal expansion of the real field. We introduce a class of Hausdorff limits, the T-infinity limits over R, that do not in general fall under the scope of Marker and Steinhorn's definability-of-types theorem. We prove that if…

Expansions in non-integer bases have been investigated abundantly since their introduction by R\'enyi. It was discovered by Erd\H{o}s et al. that the sets of numbers with a unique expansion have a much more complex structure than in the…

Let $\{X(t) : t \in \mathbb{R}^d \}$ be a multivariate operator-self-similar random field with values in $\mathbb{R}^m$. Such fields were introduced in [24] and satisfy the scaling property $\{X(c^E t) : t \in \mathbb{R}^d \} \stackrel{\rm…

The limitations of three-dimensional semi-classical gravity are explored in the context of a conformally invariant theory for a self-interacting scalar field. The analysis of the theory's scaling behaviour reveals that scalar-loop effects…

The growth and dynamics of solid surfaces displays a multitude of power law relationships, which are often associated with geometric self-similarity. In many cases the mechanisms behind these power laws are comparatively trivial, and…

The effects of dissipation on the scaling properties of nonlinear discontinuous maps are investigated by analyzing the behavior of the average squared action $\left< I^2 \right>$ as a function of the $n$-th iteration of the map as well as…

We prove that if the Schwarzian norm of a given complex-valued locally univalent harmonic mapping $f$ in the unit disk is small enough, then $f$ is, indeed, globally univalent and can be extended to a quasiconformal mapping in the extended…

Zipf's law is the most common statistical distribution displaying scaling behavior. Cities, populations or firms are just examples of this seemingly universal law. Although many different models have been proposed, no general theoretical…