On the number of critical periods for planar polynomial systems of arbitrary degree

Armengol Gasull; Changjian Liu; Jiazhong Yang

doi:10.1016/j.jde.2010.01.002

On the number of critical periods for planar polynomial systems of arbitrary degree

Armengol Gasull, Changjian Liu, Jiazhong Yang

Department of Mathematics

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

16 Citations (Scopus)

Abstract

We construct a class of planar systems of arbitrary degree n having a reversible center at the origin and such that the number of critical periods on its period annulus grows quadratically with n. As far as we know, the previous results on this subject gave systems having linear growth. © 2010 Elsevier Inc.

Original language	English
Pages (from-to)	684-692
Journal	Journal of Differential Equations
Volume	249
Issue number	3
DOIs	https://doi.org/10.1016/j.jde.2010.01.002
Publication status	Published - 1 Aug 2010

Keywords

Critical periods
Hilbert's 16th problem
Period function
Primary
Reversible center
Secondary

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10.1016/j.jde.2010.01.002

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title = "On the number of critical periods for planar polynomial systems of arbitrary degree",

abstract = "We construct a class of planar systems of arbitrary degree n having a reversible center at the origin and such that the number of critical periods on its period annulus grows quadratically with n. As far as we know, the previous results on this subject gave systems having linear growth. {\textcopyright} 2010 Elsevier Inc.",

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author = "Armengol Gasull and Changjian Liu and Jiazhong Yang",

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doi = "10.1016/j.jde.2010.01.002",

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T1 - On the number of critical periods for planar polynomial systems of arbitrary degree

AU - Gasull, Armengol

AU - Liu, Changjian

AU - Yang, Jiazhong

PY - 2010/8/1

Y1 - 2010/8/1

N2 - We construct a class of planar systems of arbitrary degree n having a reversible center at the origin and such that the number of critical periods on its period annulus grows quadratically with n. As far as we know, the previous results on this subject gave systems having linear growth. © 2010 Elsevier Inc.

AB - We construct a class of planar systems of arbitrary degree n having a reversible center at the origin and such that the number of critical periods on its period annulus grows quadratically with n. As far as we know, the previous results on this subject gave systems having linear growth. © 2010 Elsevier Inc.

KW - Critical periods

KW - Hilbert's 16th problem

KW - Period function

KW - Primary

KW - Reversible center

KW - Secondary

U2 - 10.1016/j.jde.2010.01.002

DO - 10.1016/j.jde.2010.01.002

M3 - Article

VL - 249

SP - 684

EP - 692

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 3

ER -

On the number of critical periods for planar polynomial systems of arbitrary degree

Abstract

Keywords

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