X-minimal patterns and a generalization of Sharkovskiĭ's theorem
Volume 156 / 1998
Fundamenta Mathematicae 156 (1998), 33-66
DOI: 10.4064/fm-156-1-33-66
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.
