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

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Bobok J., Kuchta M.

Fundamenta Mathematicae

1998

tom 156

nr 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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Bobok J.

1 Kuchta M.

1 1998

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