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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 975–982 (Mi semr1108)  

Geometry and topology

On the set of subarcs in some non-postrcritically finite dendrites

N. V. Abrosimovabc, M. V. Chanchievad, A. V. Tetenovad

a Regional Scientific and Educational Mathematical Center, Tomsk State University, pr. Lenina, 36, 634050, Tomsk, Russia
b Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
c Novosibirsk State University, Pirogova str., 1, 630090, Novosibirsk, Russia
d Gorno-Altaysk State University, Lenkina str., 1, 649000, Gorno-Altaysk, Russia

Abstract: We construct a family ${\mathbf F}$ of non-PCF dendrites $K$ in a plane, such that for any dendrite $K\in {\mathbf F}$ all its subarcs have the same Hausdorff dimension $s$, while the set of $s$-dimensional Hausdorff measures of subarcs connecting the given point and a self-similar Cantor subset in $K$ is a Cantor discontinuum.

Keywords: self-similar dendrite, ramification point, Hausdorff dimension, postcritically finite set.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.13557.2019/13.1
This work was supported by the Ministry of Education and Science of Russia (state assignment No. 1.13557.2019/13.1).


DOI: https://doi.org/10.17377/semi.2019.16.066

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Bibliographic databases:

UDC: 515.124, 519.172
MSC: 28A80
Received November 29, 2018, published August 3, 2019
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Citation: N. V. Abrosimov, M. V. Chanchieva, A. V. Tetenov, “On the set of subarcs in some non-postrcritically finite dendrites”, Sib. Èlektron. Mat. Izv., 16 (2019), 975–982

Citation in format AMSBIB
\Bibitem{AbrChaTet19}
\by N.~V.~Abrosimov, M.~V.~Chanchieva, A.~V.~Tetenov
\paper On the set of subarcs in some non-postrcritically finite dendrites
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 975--982
\mathnet{http://mi.mathnet.ru/semr1108}
\crossref{https://doi.org/10.17377/semi.2019.16.066}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000478799200001}


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  • http://mi.mathnet.ru/eng/semr/v16/p975

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