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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2017, Volume 14, Pages 737–751
DOI: https://doi.org/10.17377/semi.2017.14.063 (Mi semr820) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Geometry and topology

Self-similar dendrites generated by polygonal systems in the plane

M. Samuela, A. Tetenovbc, D. Vaulinb

a Department of Mathematics, Bharatha Mata College, Kochi, India
b Gorno-Altaisk State University
c Novosibirsk State University
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DOI: https://doi.org/10.17377/semi.2017.14.063
Abstract: We define a class of self-similar dendrites in $\mathbb{R}^2$ generated by system $\mathcal{S}$ of similarity maps of a convex polygon $P$ and find upper bound for the order of their ramification points, show that such dendrites are continua of bounded turning and prove Hölder continuity of their isomorphisms.
Keywords: dendrite, ramification point, self-similar set, post-critically finite sets.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00414_а
The work is supported by RFBR (grant 16-01-00414 A).
Received May 17, 2017, published August 1, 2017
Bibliographic databases:
Document Type: Article
UDC: 515.124; 519.172
MSC: 28A80; 54F50
Language: English
Citation: M. Samuel, A. Tetenov, D. Vaulin, “Self-similar dendrites generated by polygonal systems in the plane”, Sib. Èlektron. Mat. Izv., 14 (2017), 737–751
Citation in format AMSBIB
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\by M.~Samuel, A.~Tetenov, D.~Vaulin
\paper Self-similar dendrites generated by polygonal systems in the plane
\jour Sib. \`Elektron. Mat. Izv.
\yr 2017
\vol 14
\pages 737--751
\mathnet{http://mi.mathnet.ru/semr820}
\crossref{https://doi.org/10.17377/semi.2017.14.063}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000407792200063}
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