Results 21 to 30 of about 2,769 (160)

Assouad type dimensions and homogeneity of fractals [PDF]

, 2013
We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural `dimension pair'. In particular, we compute these dimensions for certain classes of self-affine sets and quasi-self-similar sets and study ...
Fraser, Jonathan M.
core   +3 more sources

Apollonian circle packings: Dynamics and Number theory [PDF]

, 2014
We give an overview of various counting problems for Apollonian circle packings, which turn out to be related to problems in dynamics and number theory for thin groups.
Oh, Hee
core   +1 more source

A φ-Contractivity and Associated Fractal Dimensions

Fractal and Fractional
In this paper, we extend the concept of dimension of sets to some general frameworks relative to a gauge function φ, where two simultaneous dimensions are introduced.
Nifeen H. Altaweel, Olayan Albalawi, Razan Albalawi   +2 more
doaj   +1 more source

Rate of convergence: the packing and centered Hausdoff measures of totally disconnected self-similar sets

, 2016
In this paper we obtain the rates of convergence of the algorithms given in [13] and [14] for an automatic computation of the centered Hausdorff and packing measures of a totally disconnected self-similar set.
Llorente, Marta, Mera, M. Eugenia, Moran, Manuel   +2 more
core   +1 more source

The Hausdorff and packing measure of some digital expansions

Acta Arithmetica, 2022
Minor changes.
openaire   +3 more sources

The Hausdorff measure and the packing measure on a perturbed Cantor set [PDF]

Real Analysis Exchange, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +4 more sources

New Insights into the Multifractal Formalism of Branching Random Walks on Galton–Watson Tree

Mathematics
In the present work, we consider three branching random walk SnZ(t),Z∈{X,Y,Φ} on a supercritical random Galton–Watson tree ∂T. We compute the Hausdorff and packing dimensions of the level set Eχ(α,β)=t∈∂T:limn→∞SnX(t)SnY(t)=αandlimn→∞SnY(t)n=β, where ∂T ...
Najmeddine Attia
doaj   +1 more source

Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley   +1 more source

Multifractal Structure of Irregular Sets via Weighted Random Sequences

Fractal and Fractional
We study the multifractal structure of irregular sets arising from Fibonacci-weighted sums of sequences of random variables. Focusing on Cantor-type subsets Kε of the unit interval, we construct sequences of free and forced blocks, where the free blocks ...
Najmeddine Attia, Taoufik Moulahi
doaj   +1 more source

Fractal properties of the random string processes

, 2006
Let $\{u_t(x),t\ge 0, x\in {\mathbb{R}}\}$ be a random string taking values in ${\mathbb{R}}^d$, specified by the following stochastic partial differential equation [Funaki (1983)]: \[\frac{\partial u_t(x)}{\partial t}=\frac{{\partial}^2u_t(x)}{\partial ...
Wu, Dongsheng, Xiao, Yimin
core   +3 more sources