Linear estimation of the number of zeros of Abelian integrals for some cubic isochronous centers

Chengzhi Li; Weigu Li; Jaume Llibre; Zhifen Zhang

doi:10.1006/jdeq.2001.4064

Linear estimation of the number of zeros of Abelian integrals for some cubic isochronous centers

Chengzhi Li, Weigu Li, Jaume Llibre, Zhifen Zhang

Department of Mathematics

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

28 Citations (Scopus)

Abstract

This paper consists of two parts. In the first part we study the relationship between conic centers (all orbits near a singular point of center type are conics) and isochronous centers of polynomial systems. In the second part we study the number of limit cycles that bifurcate from the periodic orbits of cubic reversible isochronous centers having all their orbits formed by conics, when we perturb such systems inside the class of all polynomial systems of degree n. © 2002 Elsevier Science (USA).

Original language	English
Pages (from-to)	307-333
Journal	Journal of Differential Equations
Volume	180
DOIs	https://doi.org/10.1006/jdeq.2001.4064
Publication status	Published - 10 Apr 2002

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title = "Linear estimation of the number of zeros of Abelian integrals for some cubic isochronous centers",

abstract = "This paper consists of two parts. In the first part we study the relationship between conic centers (all orbits near a singular point of center type are conics) and isochronous centers of polynomial systems. In the second part we study the number of limit cycles that bifurcate from the periodic orbits of cubic reversible isochronous centers having all their orbits formed by conics, when we perturb such systems inside the class of all polynomial systems of degree n. {\textcopyright} 2002 Elsevier Science (USA).",

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AU - Li, Chengzhi

AU - Li, Weigu

AU - Llibre, Jaume

AU - Zhang, Zhifen

PY - 2002/4/10

Y1 - 2002/4/10

N2 - This paper consists of two parts. In the first part we study the relationship between conic centers (all orbits near a singular point of center type are conics) and isochronous centers of polynomial systems. In the second part we study the number of limit cycles that bifurcate from the periodic orbits of cubic reversible isochronous centers having all their orbits formed by conics, when we perturb such systems inside the class of all polynomial systems of degree n. © 2002 Elsevier Science (USA).

AB - This paper consists of two parts. In the first part we study the relationship between conic centers (all orbits near a singular point of center type are conics) and isochronous centers of polynomial systems. In the second part we study the number of limit cycles that bifurcate from the periodic orbits of cubic reversible isochronous centers having all their orbits formed by conics, when we perturb such systems inside the class of all polynomial systems of degree n. © 2002 Elsevier Science (USA).

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DO - 10.1006/jdeq.2001.4064

M3 - Article

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VL - 180

SP - 307

EP - 333

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Linear estimation of the number of zeros of Abelian integrals for some cubic isochronous centers

Abstract

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