scholarly journals Center problem for cubic differential systems with the line at infinity of multiplicity four

2021 ◽  
Vol 38 (1) ◽  
pp. 217-222
Author(s):  
ALEXANDRU ȘUBĂ ◽  
Keyword(s):  
Center Problem ◽  
Differential Systems

In this paper the center problem for cubic differential systems with the line at infinity of multiplicity four is solved.

scholarly journals Center problem for Λ–Ω differential systems

2019 ◽  
Vol 267 (11) ◽  
pp. 6409-6446 ◽  
Author(s):  
Jaume Llibre ◽  
Rafael Ramírez ◽  
Valentín Ramírez
Keyword(s):  
Center Problem ◽  
Differential Systems

scholarly journals CENTER PROBLEM FOR CUBIC DIFFERENTIAL SYSTEMS WITH THE LINE AT INFINITY AND AN AFFINE REAL INVARIANT STRAIGHT LINE OF TOTAL MULTIPLICITY FOUR

2021 ◽  
Vol 9 (2) ◽  
pp. 35-52
Author(s):  
A. Șubă ◽  
O. Vacaraș
Keyword(s):  
Critical Point ◽  
Center Problem ◽  
Differential Systems ◽  
Straight Line ◽  
Total Multiplicity

In this article, we show that a non-degenerate monodromic critical point of differential systems with the line at infinity and an affine real invariant straight line of total multiplicity four is a center type if and only if the first four Lyapunov quantities vanish.

scholarly journals Centers: their integrability and relations with the divergence

2016 ◽  
Vol 1 (1) ◽  
pp. 79-86 ◽  
Author(s):  
J. Llibre
Keyword(s):  
Differential System ◽  
Difficult Problem ◽  
Center Problem ◽  
Differential Systems ◽  
Different Types

AbstractThis is a brief survey on the centers of the analytic differential systems in ℝ2. First we consider the kind of integrability of the different types of centers, and after we analyze the focus–center problem, i.e. how to distinguish a center from a focus. This is a difficult problem which is not completely solved. We shall present some recent results using the divergence of the differential system.

scholarly journals THE NONDEGENERATE CENTER PROBLEM IN CERTAIN FAMILIES OF PLANAR DIFFERENTIAL SYSTEMS

2009 ◽  
Vol 19 (01) ◽  
pp. 435-443 ◽  
Author(s):  
JAUME GINÉ ◽  
PAZ DE PRADA
Keyword(s):  
Limit Cycles ◽  
Center Problem ◽  
Differential Systems ◽  
The Family ◽  
Fine Focus ◽  
Isochronous Centers

This paper concerns the nondegenerate center problem in certain families of differential systems in ℝ2. We study the existence of uniformly isochronous centers and the form of their commutators. We also classify all centers of the family of the BiLiénard systems of degree five and the maximum number of limit cycles which can bifurcate from a fine focus.

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