Related papers: Fractal Measures, p-Adic Numbers And Continues Tra…
We consider the family of CIFSs of generalized complex continued fractions with a complex parameter space. This is a new interesting example to which we can apply a general theory of infinite CIFSs and analytic families of infinite CIFSs.…
For fixed natural numbers $r$ and $s$, where $2\leq s \leq r$, we consider a representation of numbers from the interval $[0;\frac{r}{s-1}]$ obtained by encoding numbers by means of the alphabet $A=\{0,1,...,r\}$ via the expansion…
We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate the persistent homology dimension, and compare its performance…
The Hausdorff dimensions of the Julia sets for non-analytic maps: f(z) = z^2 + epsilon z^* and f(z) = {z^*}^2 + epsilon are calculated perturbatively for small epsilon. It is shown that Ruelle's formula for Hausdorff dimensions of analytic…
We study ordinary, zero-form symmetry $G$ and its anomalies in a system with a one-form symmetry $\Gamma$. In a theory with one-form symmetry, the action of $G$ on charged line operators is not completely determined, and additional data, a…
A contribution is presented to the study of hadron spectroscopy through the use of fractals and discrete scale invariance implying log-periodic corrections to continuous scaling. The masses of mesons and baryons, reported by the Particle…
In this work we are interested in the self--affine fractals studied by Gatzouras and Lalley and by the author which generalize the famous general Sierpinski carpets studied by Bedford and McMullen. We give a formula for the Hausdorff…
Building on the development of [MOR13], bifurcation of unstable modes that emerge from continuous spectra in a class of infinite-dimensional noncanonical Hamiltonian systems is investigated. Of main interest is a bifurcation termed the…
The Cantor set complementary to the Devil's Staircase associated with the Circle Map has a fractal dimension d approximately equal to 0.87, a value that is universal for a wide range of maps, such results being of a numerical character. In…
It is well known that the spectral form factor (SFF) of a possibly degenerate many-body Hamiltonian can be identified with a planar random walk taking steps of unequal length. In this paper we push this identification further and propose to…
Let $K$ be an uncountable compact metric space and let $C(K,\mathbb{R}^d)$ denote the set of continuous maps $f\colon K \to \mathbb{R}^d$ endowed with the maximum norm. The goal of this paper is to determine various fractal dimensions of…
The image fractal analysis is actively used in all science branches. In particular in materials science the fractal analysis is applied to study microstructure of deformed metals because its structure can be interpreted as the fractal…
We develop the theory of multiresolutions in the context of Hausdorff measure of fractional dimension between 0 and 1. While our fractal wavelet theory has points of similarity that it shares with the standard case of Lebesgue measure on…
In 1928, Jarn\'{\i}k \cite{Jar} obtained that the set of continued fractions with bounded coefficients has Hausdorff dimension one. Good \cite{Goo} observed a dimension drop phenomenon by proving that the Hausdorff dimension of the set of…
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…
We show that the fractonic dipole-conserving algebra can be obtained as an Aristotelian (and pseudo-Carrollian) contraction of the Poincar\'e algebra in one dimension higher. Such contraction allows to obtain fracton electrodynamics from a…
The Directed Landscape, a random directed metric on the plane (where the first and the second coordinates are termed spatial and temporal respectively), was constructed in the breakthrough work of Dauvergne, Ortmann, and Vir\'ag, and has…
Motivated by the study of attractors in the Kuramoto model (KM) on graphs approximating the Sierpinski gasket (SG), we revisit the problem of harmonic maps (HMs) from SG to the circle, first considered by Strichartz. We provide a geometric…
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…
Fractal geometry of critical curves appearing in 2D critical systems is characterized by their harmonic measure. For systems described by conformal field theories with central charge $c\leqslant 1$, scaling exponents of harmonic measure…