An extension of Sharkovsky's theorem to periodic difference equations

Ziyad AlSharawi; James Angelos; Saber Elaydi; Leela Rakesh

doi:10.1016/j.jmaa.2005.04.059

An extension of Sharkovsky's theorem to periodic difference equations

Ziyad AlSharawi, James Angelos, Saber Elaydi, Leela Rakesh

Mathematics

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

50 Scopus citations

Abstract

We present an extension of Sharkovsky's theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric cycle with or without stability properties.

Original language	English
Pages (from-to)	128-141
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	316
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2005.04.059
State	Published - Apr 1 2006

Keywords

Difference equations
Geometric cycles
Nonautonomous
Periodic orbits
Skew-product dynamical systems

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10.1016/j.jmaa.2005.04.059

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title = "An extension of Sharkovsky's theorem to periodic difference equations",

abstract = "We present an extension of Sharkovsky's theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric cycle with or without stability properties.",

keywords = "Difference equations, Geometric cycles, Nonautonomous, Periodic orbits, Skew-product dynamical systems",

author = "Ziyad AlSharawi and James Angelos and Saber Elaydi and Leela Rakesh",

year = "2006",

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T1 - An extension of Sharkovsky's theorem to periodic difference equations

AU - AlSharawi, Ziyad

AU - Angelos, James

AU - Elaydi, Saber

AU - Rakesh, Leela

PY - 2006/4/1

Y1 - 2006/4/1

N2 - We present an extension of Sharkovsky's theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric cycle with or without stability properties.

AB - We present an extension of Sharkovsky's theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric cycle with or without stability properties.

KW - Difference equations

KW - Geometric cycles

KW - Nonautonomous

KW - Periodic orbits

KW - Skew-product dynamical systems

UR - http://www.scopus.com/inward/record.url?scp=29944434032&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2005.04.059

DO - 10.1016/j.jmaa.2005.04.059

M3 - Article

AN - SCOPUS:29944434032

SN - 0022-247X

VL - 316

SP - 128

EP - 141

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

An extension of Sharkovsky's theorem to periodic difference equations

Abstract

Keywords

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