Homogeneous-Like Generalized Cubic Systems
Author
Source
International Journal of Differential Equations
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-09-05
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
We consider properties and center conditions for plane polynomial systems of the forms x˙=-y-p1(x,y)-p2(x,y), y˙=x+q1(x,y)+q2(x,y) where p1, q1 and p2, q2 are polynomials of degrees n and 2n-1, respectively, for integers n≥2.
We restrict our attention to those systems for which yp2(x,y)+xq2(x,y)=0.
In this case the system can be transformed to a trigonometric Abel equation which is similar in form to the one obtained for homogeneous systems (p2=q2=0).
From this we show that any center condition of a homogeneous system for a given n can be transformed to a center condition of the corresponding generalized cubic system and we use a similar idea to obtain center conditions for several other related systems.
As in the case of the homogeneous system, these systems can also be transformed to Abel equations having rational coefficients and we briefly discuss an application of this to a particular Abel equation.
American Psychological Association (APA)
Nicklason, G. R.. 2016. Homogeneous-Like Generalized Cubic Systems. International Journal of Differential Equations،Vol. 2016, no. 2016, pp.1-15.
https://search.emarefa.net/detail/BIM-1105714
Modern Language Association (MLA)
Nicklason, G. R.. Homogeneous-Like Generalized Cubic Systems. International Journal of Differential Equations No. 2016 (2016), pp.1-15.
https://search.emarefa.net/detail/BIM-1105714
American Medical Association (AMA)
Nicklason, G. R.. Homogeneous-Like Generalized Cubic Systems. International Journal of Differential Equations. 2016. Vol. 2016, no. 2016, pp.1-15.
https://search.emarefa.net/detail/BIM-1105714
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1105714