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Self-similar Jordan arcs and the graph directed systems of similarities

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Abstract

We study the attractors \(\vec \gamma \) of finite graph directed systems S of contracting similarities in ℝd whose components are Jordan arcs. We prove that every self-similar Jordan arc different from a straight line segment may be partitioned into finitely many nonoverlapping subarcs δj each of which also admits a partition into nonoverlapping images of subarcs δj under contracting similarities. A formal description for this property is given by the multizipper construction.

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Authors and Affiliations

  1. Gorno-Altaisk State University, Gorno-Altaisk, Russia

    A. V. Tetenov

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  1. A. V. Tetenov
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__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 5, pp. 1147–1159, September–October, 2006.

Original Russian Text Copyright © 2006 Tetenov A. V.

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Tetenov, A.V. Self-similar Jordan arcs and the graph directed systems of similarities. Sib Math J 47, 940–949 (2006). https://doi.org/10.1007/s11202-006-0105-7

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  • DOI: https://doi.org/10.1007/s11202-006-0105-7

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