Minimal periodic orbits for continous maps of the interval

Lluis Alseda; Jaume Llibre; Rafel Serra

doi:10.1090/S0002-9947-1984-0760976-5

Minimal periodic orbits for continous maps of the interval

Lluis Alseda, Jaume Llibre, Rafel Serra

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

11 Citations (Scopus)

Abstract

For continuous maps of the interval into itself, Sarkovskii’s Theorem gives the notion of minimal periodic orbit. We complete the characterization of the behavior of minimal periodic orbits. Also, we show for unimodal maps that the min-max essentially describes the behavior of minimal periodic orbits. © 1984 American Mathematical Society.

Original language	English
Pages (from-to)	595-627
Journal	Transactions of the American Mathematical Society
Volume	286
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1984-0760976-5
Publication status	Published - 1 Jan 1984

Keywords

Min-max
Minimal periodic orbit
Periodic point
Simple periodic orbit
Unimodal map

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10.1090/S0002-9947-1984-0760976-5

Cite this

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title = "Minimal periodic orbits for continous maps of the interval",

abstract = "For continuous maps of the interval into itself, Sarkovskii{\textquoteright}s Theorem gives the notion of minimal periodic orbit. We complete the characterization of the behavior of minimal periodic orbits. Also, we show for unimodal maps that the min-max essentially describes the behavior of minimal periodic orbits. {\textcopyright} 1984 American Mathematical Society.",

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AU - Llibre, Jaume

AU - Serra, Rafel

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AB - For continuous maps of the interval into itself, Sarkovskii’s Theorem gives the notion of minimal periodic orbit. We complete the characterization of the behavior of minimal periodic orbits. Also, we show for unimodal maps that the min-max essentially describes the behavior of minimal periodic orbits. © 1984 American Mathematical Society.

KW - Min-max

KW - Minimal periodic orbit

KW - Periodic point

KW - Simple periodic orbit

KW - Unimodal map

U2 - 10.1090/S0002-9947-1984-0760976-5

DO - 10.1090/S0002-9947-1984-0760976-5

M3 - Article

VL - 286

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ER -

Minimal periodic orbits for continous maps of the interval

Abstract

Keywords

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