Geodesic
X-minimal patterns and a generalization of Sharkovskiĭ's theorem
Fundamenta Mathematicae, Tome 156 (1998) no. 1, pp. 33-66 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm-156-1-33-66
Keywords: iteration, periodic orbit, cycle, pattern, minimal, forcing relation, Sharkovskiĭ s theorem

Jozef Bobok 1 ; Milan Kuchta 1

1 
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Jozef Bobok; Milan Kuchta. X-minimal patterns and a generalization of Sharkovskiĭ's theorem. Fundamenta Mathematicae, Tome 156 (1998) no. 1, pp. 33-66. doi: 10.4064/fm-156-1-33-66

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