Z. Buczolich

activity

20032026

most citedTopological Hausdorff dimension and level sets of generic continuous functions on fractals

30 citations · 58 across the 25 of their papers we have counts for

collaborators

Showing math.DSShow all

12 papers · 1 filter

math.DS2026

Dynamics of the Takagi function and the shadowing property

Zoltán Buczolich, Jesús Llorente

The Takagi function $T : [0, 1] \to R$ is a classical example of a continuous nowhere differentiable function. In this paper, we study the discrete dynamical system generated…

math.DS2019

Divergence of weighted square averages in $L^{1}$

Zoltán Buczolich, Tanja Eisner

We study convergence of ergodic averages along squares with polynomial weights. For a given polynomial $P \in Z [\cdot]$ , consider the set of all $θ \in [0, 1)$ such that for e…

math.DS2019

Generic Birkhoff Spectra

Zoltán Buczolich, Balázs Maga, Ryo Moore

Suppose that $Ω = {0, 1}^{N}$ and $σ$ is the one-sided shift. The Birkhoff spectrum $ \displaystyle S_{f}( α)=\dim_{H}\Big \{ ω\in Ω:\lim_{N \to \infty} \frac{1}{N} \s…

math.DS2019

Fast and slow points of Birkhoff sums

Frédéric Bayart, Zoltan Buczolich, Yanick Heurteaux

We investigate the growth rate of the Birkhoff sums $S_{n, α} f (x) = \sum_{k = 0}^{n - 1} f (x + k α)$ , where $f$ is a continuous function with zero mean defined on the unit circle $\mathbb T…

math.DS2018

Isentropes and Lyapunov exponents

Zoltán Buczolich, Gabriella Keszthelyi

We consider skew tent maps $T_{α, β} (x)$ such that $(α, β) \in [0, 1]^{2}$ is the turning point of $T_{α, β}$ , that is, $T_{α, β} = \frac{β}{α} x$ for $0 \leq x \leq α$ and $T_{α, β…

math.DS2016

Ergodic averages with prime divisor weights in $L^{1}$

Zoltan Buczolich

We show that $ω (n)$ and $Ω (n)$ , the number of distinct prime factors of $n$ and the number of distinct prime factors of $n$ counted according to multiplicity are good weigh…

Dynamics of the Takagi function and the shadowing property

Divergence of weighted square averages in L1

Generic Birkhoff Spectra

Fast and slow points of Birkhoff sums

Isentropes and Lyapunov exponents

Ergodic averages with prime divisor weights in L1

Divergence of weighted square averages in $L^{1}$

Ergodic averages with prime divisor weights in $L^{1}$