Rafał Tryniecki

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math.DS2026

Asymptotics of the Hausdorff measure for the Gauss map and its linearized analogue

RafaÅ Tryniecki, Mariusz UrbaÅski, Anna Zdunik

Let $G (x) := {1/ x}$ be the Gauss map. By $g_{n} (x) = \frac{1}{x + n}$ we denote its continuous/real analytic inverse branches. We define iterated function system (IFS) $G_{n}$ by limiting…

math.DS2026

On the conditions for the continuity of the Hausdorff measure

RafaÅ Tryniecki

Let $(b_{k})_{k = 0}^{\infty}$ be strictly decreasing sequence of real numbers such that $b_{0} = 1$ and ${f_{k} : [b_{k}, b_{k - 1}] \to [0, 1]}_{k \in N}$ be decreasing functions such that $f_k(…

math.DS2024

Packing measure of the linear Gauss system

RafaÅ Tryniecki

For every $k \in N$ let $f_{k} : [\frac{1}{k + 1}, \frac{1}{k}] \to [0, 1]$ be decreasing, linear functions such that $f_{k} (\frac{1}{k + 1}) = 1$ and $f_{k} (\frac{1}{k}) = 0$ , $k = 1,…