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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Self-similar sets and self-similar measures in the p-adics
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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