Self-similar sets and self-similar measures in the p-adics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489830" target="_blank" >RIV/00216208:11320/24:10489830 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=LYq5M_Btom" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=LYq5M_Btom</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4171/JFG/154" target="_blank" >10.4171/JFG/154</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Self-similar sets and self-similar measures in the p-adics

Popis výsledku v původním jazyce

In this paper, we investigate p-adic self-similar sets and p-adic self-similar measures. We introduce a condition (C) under which p-adic self-similar sets can be shown to have a number of nice properties. It is shown that p-adic self-similar sets satisfying condition (C) are p-adic path set fractals. This allows us to easily compute the Hausdorff dimension of these sets. We further show that the set of p-adic path set fractals is strictly larger than this set of p-adic self-similar sets. The directed graph associated to p-adic self-similar sets satisfying condition (C) is shown to have a unique essential class. Moreover, it is shown that almost all points are eventually in the essential class. For p-adic self-similar measures satisfying this condition, we show that many results involving local dimension are similar to those of their real counterparts, with fewer complications. We next study the more general p-adic path set fractals, first showing that the existence of an interior point is equivalent to the set having Hausdorff dimension 1 . We further show that often the decimation of p-adic path set fractals results in a set with maximal Hausdorff dimension.

Název v anglickém jazyce

Self-similar sets and self-similar measures in the p-adics

Popis výsledku anglicky

In this paper, we investigate p-adic self-similar sets and p-adic self-similar measures. We introduce a condition (C) under which p-adic self-similar sets can be shown to have a number of nice properties. It is shown that p-adic self-similar sets satisfying condition (C) are p-adic path set fractals. This allows us to easily compute the Hausdorff dimension of these sets. We further show that the set of p-adic path set fractals is strictly larger than this set of p-adic self-similar sets. The directed graph associated to p-adic self-similar sets satisfying condition (C) is shown to have a unique essential class. Moreover, it is shown that almost all points are eventually in the essential class. For p-adic self-similar measures satisfying this condition, we show that many results involving local dimension are similar to those of their real counterparts, with fewer complications. We next study the more general p-adic path set fractals, first showing that the existence of an interior point is equivalent to the set having Hausdorff dimension 1 . We further show that often the decimation of p-adic path set fractals results in a set with maximal Hausdorff dimension.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Fractal Geometry

ISSN

2308-1309

e-ISSN

2308-1317

Svazek periodika

11

Číslo periodika v rámci svazku

3-4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

41

Strana od-do

247-287

Kód UT WoS článku

001343949200003

EID výsledku v databázi Scopus

2-s2.0-85208364441