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ArticleOriginal scientific text

Title

X-minimal patterns and a generalization of Sharkovskiĭ's theorem

Authors 1, 2

Affiliations

  1. KM FSv. ČVUT, Thákurova 7, 166 29 Praha 6, Czech Republic
  2. athematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovak Republic

Abstract

We study the law of coexistence of different types of cycles for a continuous map of the interval. For this we introduce the notion of eccentricity of a pattern and characterize those patterns with a given eccentricity that are simplest from the point of view of the forcing relation. We call these patterns X-minimal. We obtain a generalization of Sharkovskiĭ's Theorem where the notion of period is replaced by the notion of eccentricity.

Keywords

ENG
iteration, periodic orbit, cycle, pattern, minimal, forcing relation, Sharkovskiĭ s theorem

Bibliography

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Fundamenta Mathematicae
1998/156/1
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Pages:
33-66
Main language of publication
English
Received
1996-10-24
Accepted
1997-04-22
Published
1998
Exact and natural sciences