Centers and Uniform Isochronous Centers of Planar Polynomial Differential Systems
نویسندگان
چکیده
منابع مشابه
Uniformly Isochronous Polynomial Centers
We study a specific family of uniformly isochronous polynomial systems. Our results permit us to solve a problem about centers of such systems. We consider the composition conjecture for uniformly isochronous polynomial systems.
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In this paper we classify the global phase portraits in the Poincaré disc of all quartic polynomial differential systems with a uniform isochronous center at the origin.
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In this paper we completed the classification of the phase portraits in the Poincaré disc of uniform isochronous cubic and quartic centers previously studied by several authors. There are three and fourteen different topological phase portraits for the uniform isochronous cubic and quartic centers respectively.
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We study the number of limit cycles of T−periodic Chini equations and some generalized Abel equations and apply the results obtained to illustrate the existence of isochronous centers in three-dimensional autonomous differential systems. Mathematics Subject Classification (2000). Primary: 34C25; Secondary: 37C10, 37C27.
متن کاملCenters and isochronous centers for generalized quintic systems
In this paper we classify the centers and the isochronous centers of certain polynomial differential systems in R2 of degree d ≥ 5 odd that in complex notation can be written as ż = (λ+ i)z + (zz̄) d−5 2 (Az +Bzz̄ + Czz̄ +Dzz̄ + Ezz̄ + F z̄), where λ ∈ R and A,B,C,D,E, F ∈ C. Note that if d = 5 we obtain the full class of polynomial differential systems of the form a linear system with homogeneous po...
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ژورنال
عنوان ژورنال: Journal of Dynamics and Differential Equations
سال: 2018
ISSN: 1040-7294,1572-9222
DOI: 10.1007/s10884-018-9672-0