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.
@article{bwmeta1.element.bwnjournal-article-fmv156i1p33bwm,
author = {Jozef Bobok and Milan Kuchta},
title = {X-minimal patterns and a generalization of Sharkovski\u\i 's theorem},
journal = {Fundamenta Mathematicae},
volume = {158},
year = {1998},
pages = {33-66},
zbl = {0909.26003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv156i1p33bwm}
}
Bobok, Jozef; Kuchta, Milan. X-minimal patterns and a generalization of Sharkovskiĭ's theorem. Fundamenta Mathematicae, Tome 158 (1998) pp. 33-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv156i1p33bwm/
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