Topological contractive systems

M. Barnsley; K. Igudesman

doi:10.1134/S1995080211030048

Topological contractive systems

M. Barnsley^*, K. Igudesman

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We are concerned with one of the fundamental problems of fractal geometry: When is a topological contractive system a metric contractive system? We show that there exists a metric such that a topological contractive system is nonexpansive and give a sufficient condition for the contractive property of this system.

Original language	English
Pages (from-to)	220-223
Number of pages	4
Journal	Lobachevskii Journal of Mathematics
Volume	32
Issue number	3
DOIs	https://doi.org/10.1134/S1995080211030048
Publication status	Published - Jul 2011

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title = "Topological contractive systems",

abstract = "We are concerned with one of the fundamental problems of fractal geometry: When is a topological contractive system a metric contractive system? We show that there exists a metric such that a topological contractive system is nonexpansive and give a sufficient condition for the contractive property of this system.",

keywords = "Contraction, attractor, iterated function systems, metric structures, pseudodistance",

author = "M. Barnsley and K. Igudesman",

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AB - We are concerned with one of the fundamental problems of fractal geometry: When is a topological contractive system a metric contractive system? We show that there exists a metric such that a topological contractive system is nonexpansive and give a sufficient condition for the contractive property of this system.

KW - Contraction

KW - attractor

KW - iterated function systems

KW - metric structures

KW - pseudodistance

UR - https://www.scopus.com/pages/publications/80051891592

U2 - 10.1134/S1995080211030048

DO - 10.1134/S1995080211030048

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JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

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Topological contractive systems

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