This article is cited in 3 papers

Geometry and topology

Self-similar dendrites generated by polygonal systems in the plane

M. Samuel^a, A. Tetenov^bc, D. Vaulin<sup>b

a</sup> Department of Mathematics, Bharatha Mata College, Kochi, India
^b Gorno-Altaisk State University
^c Novosibirsk State University

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.

UDC: 515.124; 519.172

MSC: 28A80; 54F50

Received May 17, 2017, published August 1, 2017

Language: English

DOI: 10.17377/semi.2017.14.063

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