Centers and Isochronous Centers for Two Classes of Generalized Seventh and Ninth Systems

Jaume Llibre; Clàudia Valls

doi:https://doi.org/10.1007/s10884-010-9175-0

Centers and Isochronous Centers for Two Classes of Generalized Seventh and Ninth Systems

Jaume Llibre, Clàudia Valls

Department of Mathematics

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

8 Citations (Scopus)

Abstract

We classify new classes of centers and of isochronous centers for polynomial differential systems in ℝ2 of arbitrary odd degree d ≥ 7 that in complex notation z = x + iy can be written as where j is either 0 or 1, λ ε ℝ and A,B,C ε ℂ. Note that if j = 0 and d = 7 we obtain a special case of seventh polynomial differential systems which can have a center at the origin, and if j = 1 and d = 9 we obtain a special case of ninth polynomial differential systems which can have a center at the origin. © 2010 Springer Science+Business Media, LLC.

Original language	English
Pages (from-to)	657-675
Journal	Journal of Dynamics and Differential Equations
Volume	22
Issue number	4
DOIs	https://doi.org/10.1007/s10884-010-9175-0
Publication status	Published - 1 Apr 2010

Keywords

Centers
Isochronous
Polynomial vector fields

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T1 - Centers and Isochronous Centers for Two Classes of Generalized Seventh and Ninth Systems

AU - Llibre, Jaume

AU - Valls, Clàudia

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N2 - We classify new classes of centers and of isochronous centers for polynomial differential systems in ℝ2 of arbitrary odd degree d ≥ 7 that in complex notation z = x + iy can be written as where j is either 0 or 1, λ ε ℝ and A,B,C ε ℂ. Note that if j = 0 and d = 7 we obtain a special case of seventh polynomial differential systems which can have a center at the origin, and if j = 1 and d = 9 we obtain a special case of ninth polynomial differential systems which can have a center at the origin. © 2010 Springer Science+Business Media, LLC.

AB - We classify new classes of centers and of isochronous centers for polynomial differential systems in ℝ2 of arbitrary odd degree d ≥ 7 that in complex notation z = x + iy can be written as where j is either 0 or 1, λ ε ℝ and A,B,C ε ℂ. Note that if j = 0 and d = 7 we obtain a special case of seventh polynomial differential systems which can have a center at the origin, and if j = 1 and d = 9 we obtain a special case of ninth polynomial differential systems which can have a center at the origin. © 2010 Springer Science+Business Media, LLC.

KW - Centers

KW - Isochronous

KW - Polynomial vector fields

UR - https://ddd.uab.cat/record/226095

U2 - https://doi.org/10.1007/s10884-010-9175-0

DO - https://doi.org/10.1007/s10884-010-9175-0

M3 - Article

VL - 22

SP - 657

EP - 675

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

SN - 1040-7294

IS - 4

ER -