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

Fundamenta Mathematicae (1998)

- Volume: 156, Issue: 1, page 33-66
- ISSN: 0016-2736

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topBobok, Jozef, and Kuchta, Milan. "X-minimal patterns and a generalization of Sharkovskiĭ's theorem." Fundamenta Mathematicae 156.1 (1998): 33-66. <http://eudml.org/doc/212260>.

@article{Bobok1998,

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.},

author = {Bobok, Jozef, Kuchta, Milan},

journal = {Fundamenta Mathematicae},

keywords = {iteration; periodic orbit; cycle; pattern; minimal; forcing relation; Sharkovskiĭ s theorem; cycles; Sharkovskij's theorem},

language = {eng},

number = {1},

pages = {33-66},

title = {X-minimal patterns and a generalization of Sharkovskiĭ's theorem},

url = {http://eudml.org/doc/212260},

volume = {156},

year = {1998},

}

TY - JOUR

AU - Bobok, Jozef

AU - Kuchta, Milan

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

JO - Fundamenta Mathematicae

PY - 1998

VL - 156

IS - 1

SP - 33

EP - 66

AB - 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.

LA - eng

KW - iteration; periodic orbit; cycle; pattern; minimal; forcing relation; Sharkovskiĭ s theorem; cycles; Sharkovskij's theorem

UR - http://eudml.org/doc/212260

ER -

## References

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