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

Volume 156 / 1998

Jozef Bobok, Milan Kuchta Fundamenta Mathematicae 156 (1998), 33-66 DOI: 10.4064/fm-156-1-33-66


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.


  • Jozef Bobok
  • Milan Kuchta

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