On deformation of polygonal dendrites preserving the intersection graph

Dmitry Drozdov, Mary Samuel, Andrei Tetenov

Research output: Contribution to journalArticlepeer-review

Abstract

Let S = S1, ..., Sm be a system of contracting similarities of R2. The attractor K(S) of the system S is a non-empty compact set satisfying K = S1(K) ∪ ... ∪ Sm(K). We consider contractible polygonal systems S which are defined by a finite family of polygons whose intersection graph is a tree and therefore the attractor K(S) is a dendrite. We find conditions under which a deformation S0 of a contractible polygonal system S has the same intersection graph and therefore the attractor K(S0) is a self-similar dendrite which is isomorphic to the attractor K of the system S.

Original languageEnglish
Article numberP2.07
JournalArt of Discrete and Applied Mathematics
Volume4
Issue number2
DOIs
Publication statusPublished - 17 Feb 2021

Keywords

  • Attractor
  • Generalized polygonal system
  • Index diagram
  • Intersection graph
  • Self-similar dendrite

OECD FOS+WOS

  • 1.01 MATHEMATICS
  • 1.02 COMPUTER AND INFORMATION SCIENCES

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