Zobrazeno 1 - 10
of 111
pro vyhledávání: '"Kolossváry, István"'
We study the fine local scaling properties of a class of self-affine fractal sets called Gatzouras-Lalley carpets. More precisely, we establish a formula for the Assouad spectrum of all Gatzouras-Lalley carpets as the concave conjugate of an explicit
Externí odkaz:
http://arxiv.org/abs/2401.07168
Autor:
Kolossváry, István
In this paper a sponge in $\mathbb{R}^d$ is the attractor of an iterated function system consisting of finitely many strictly contracting affine maps whose linear part is a diagonal matrix. A suitable separation condition is introduced under which a
Externí odkaz:
http://arxiv.org/abs/2205.01043
Publikováno v:
Ergodic Theory and Dynamical Systems, 43, (2023), 2974-2996
We derive upper and lower bounds for the Assouad and lower dimensions of self-affine measures in $\mathbb{R}^d$ generated by diagonal matrices and satisfying suitable separation conditions. The upper and lower bounds always coincide for $d=2,3$ yield
Externí odkaz:
http://arxiv.org/abs/2203.11247
Autor:
Banaji, Amlan, Kolossváry, István
Intermediate dimensions were recently introduced to provide a spectrum of dimensions interpolating between Hausdorff and box-counting dimensions for fractals where these differ. In particular, the self-affine Bedford-McMullen carpets are a natural ca
Externí odkaz:
http://arxiv.org/abs/2111.05625
We define a new metric between natural numbers induced by the $\ell_\infty$ norm of their unique prime signatures. In this space, we look at the natural analog of the number line and study the arithmetic function $L_\infty(N)$, which tabulates the cu
Externí odkaz:
http://arxiv.org/abs/2005.02027
Autor:
Kolossváry, István
This paper presents a general procedure based on using the method of types to calculate the box dimension of sets. The approach unifies and simplifies multiple box counting arguments. In particular, we use it to generalize the formula for the box dim
Externí odkaz:
http://arxiv.org/abs/2102.11049
This paper studies how long it takes the orbit of the chaos game to reach a certain density inside the attractor of a strictly contracting iterated function system of which we only assume that its lower dimension is positive. We show that the rate of
Externí odkaz:
http://arxiv.org/abs/2102.02047
Autor:
Kolossváry, István
The intermediate dimensions of a set $\Lambda$, elsewhere denoted by $\dim_{\theta}\Lambda$, interpolates between its Hausdorff and box dimensions using the parameter $\theta\in[0,1]$. Determining a precise formula for $\dim_{\theta}\Lambda$ is parti
Externí odkaz:
http://arxiv.org/abs/2006.14366
This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space of self-conformal IFSs, we show that generically (in topological sense) if the attractor of such a system has Haus
Externí odkaz:
http://arxiv.org/abs/2006.02412