New Family of Centers of Planar Polynomial Differential Systems of Arbitrary Even Degree

Jaume Llibre; Marzieh Mousavi; Arefeh Nabavi

doi:10.1007/s10883-019-09432-x

New Family of Centers of Planar Polynomial Differential Systems of Arbitrary Even Degree

Jaume Llibre, Marzieh Mousavi, Arefeh Nabavi

Department of Mathematics

Research output: Contribution to journal › Article › Research

1 Citation (Scopus)

Abstract

© 2019, Springer Science+Business Media, LLC, part of Springer Nature. The problem of distinguishing between a focus and a center is one of the classical problems in the qualitative theory of planar differential systems. In this paper, we provide a new family of centers of polynomial differential systems of arbitrary even degree. Moreover, we classify the global phase portraits in the Poincaré disc of the centers of this family having degree 2, 4, and 6.

Original language	English
Pages (from-to)	619-630
Journal	Journal of Dynamical and Control Systems
Volume	25
DOIs	https://doi.org/10.1007/s10883-019-09432-x
Publication status	Published - 15 Oct 2019

Keywords

Center
First integral
Invariant algebraic curve
Poincaré compactification

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Llibre, J., Mousavi, M., & Nabavi, A. (2019). New Family of Centers of Planar Polynomial Differential Systems of Arbitrary Even Degree. Journal of Dynamical and Control Systems, 25, 619-630. https://doi.org/10.1007/s10883-019-09432-x

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AB - © 2019, Springer Science+Business Media, LLC, part of Springer Nature. The problem of distinguishing between a focus and a center is one of the classical problems in the qualitative theory of planar differential systems. In this paper, we provide a new family of centers of polynomial differential systems of arbitrary even degree. Moreover, we classify the global phase portraits in the Poincaré disc of the centers of this family having degree 2, 4, and 6.

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KW - First integral

KW - Invariant algebraic curve

KW - Poincaré compactification

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