Linear type global centers of linear systems with cubic homogeneous nonlinearities

Johanna D. García-Saldaña; Jaume Llibre; Claudia Valls

doi:10.1007/s12215-019-00433-0

Linear type global centers of linear systems with cubic homogeneous nonlinearities

Johanna D. García-Saldaña, Jaume Llibre, Claudia Valls

Department of Mathematics

Research output: Contribution to journal › Article › Research

1 Citation (Scopus)

Abstract

© 2019, Springer-Verlag Italia S.r.l., part of Springer Nature. A center p of a differential system in R2 is global if R2\ { p} is filled of periodic orbits. It is known that a polynomial differential system of degree 2 has no global centers. Here we characterize the global centers of the differential systems x˙=ax+by+P3(x,y),y˙=cx+dy+Q3(x,y),with P3 and Q3 homogeneous polynomials of degree 3, and such that the center has purely imaginary eigenvalues, i.e. a linear type center.

Original language	English
Journal	Rendiconti del Circolo Matematico di Palermo
DOIs	https://doi.org/10.1007/s12215-019-00433-0
Publication status	Published - 1 Jan 2019

Keywords

Center
Cubic polynomial differential system
Global center

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title = "Linear type global centers of linear systems with cubic homogeneous nonlinearities",

abstract = "{\textcopyright} 2019, Springer-Verlag Italia S.r.l., part of Springer Nature. A center p of a differential system in R2 is global if R2\ { p} is filled of periodic orbits. It is known that a polynomial differential system of degree 2 has no global centers. Here we characterize the global centers of the differential systems x˙=ax+by+P3(x,y),y˙=cx+dy+Q3(x,y),with P3 and Q3 homogeneous polynomials of degree 3, and such that the center has purely imaginary eigenvalues, i.e. a linear type center.",

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AU - Llibre, Jaume

AU - Valls, Claudia

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N2 - © 2019, Springer-Verlag Italia S.r.l., part of Springer Nature. A center p of a differential system in R2 is global if R2\ { p} is filled of periodic orbits. It is known that a polynomial differential system of degree 2 has no global centers. Here we characterize the global centers of the differential systems x˙=ax+by+P3(x,y),y˙=cx+dy+Q3(x,y),with P3 and Q3 homogeneous polynomials of degree 3, and such that the center has purely imaginary eigenvalues, i.e. a linear type center.

AB - © 2019, Springer-Verlag Italia S.r.l., part of Springer Nature. A center p of a differential system in R2 is global if R2\ { p} is filled of periodic orbits. It is known that a polynomial differential system of degree 2 has no global centers. Here we characterize the global centers of the differential systems x˙=ax+by+P3(x,y),y˙=cx+dy+Q3(x,y),with P3 and Q3 homogeneous polynomials of degree 3, and such that the center has purely imaginary eigenvalues, i.e. a linear type center.

KW - Center

KW - Cubic polynomial differential system

KW - Global center

U2 - 10.1007/s12215-019-00433-0

DO - 10.1007/s12215-019-00433-0

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