Computing Center Conditions for Non-analytic Vector Fields with Constant Angular Speed
We investigate the planar quasi-septic non-analytic systems which have a center-focus equilibrium at the origin and whose angular speed is constant. The system could be changed into an analytic system by two transformations, with the help of computer algebra system MATHEMATICA, the conditions of uniform isochronous center are obtained.
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closed orbits for planar autonomous systems, Acta. Math. Sinica. 34
(1991),490-501.
[2] J. Chavarriga and M. Sabatini,A Survey of IsochronousCenters,Qualitative
Theory of Dynam.systems. 1, (1999),1-70.
[3] A. Algaba, M. Reyes, and A. Bravo,Geometry of the Uniformly
Isochronous Centers with Polynomial Commutators, Differential Equations
Dynamical Systems 10, (2002),257-275.
[4] A. Algaba and M. Reyes,Computing Center Conditions for Vector Fields
with Constant Angular Speed, J. Comput. Appl.Math. 154, (2003),143-
159.
[5] R.Conti,Centers of Planar Polynomial Systems, A Review,Mathematiche
2, (1998),207-240.
[6] Y. Liu, J. Li, Theory of values of singular point in complex autonomous
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[1] Y. Lin, J. Li, Normal form and critical points values of the period of
closed orbits for planar autonomous systems, Acta. Math. Sinica. 34
(1991),490-501.
[2] J. Chavarriga and M. Sabatini,A Survey of IsochronousCenters,Qualitative
Theory of Dynam.systems. 1, (1999),1-70.
[3] A. Algaba, M. Reyes, and A. Bravo,Geometry of the Uniformly
Isochronous Centers with Polynomial Commutators, Differential Equations
Dynamical Systems 10, (2002),257-275.
[4] A. Algaba and M. Reyes,Computing Center Conditions for Vector Fields
with Constant Angular Speed, J. Comput. Appl.Math. 154, (2003),143-
159.
[5] R.Conti,Centers of Planar Polynomial Systems, A Review,Mathematiche
2, (1998),207-240.
[6] Y. Liu, J. Li, Theory of values of singular point in complex autonomous
differential system. Sci. China (Series A) 3 (1989),245-255.
[7] R.Conti,uniform isochronous centers of polynomial systems in R2, Lecture
Notes in Pure and Appl.Math 152 (1994),21-31.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56379", author = "Li Feng", title = "Computing Center Conditions for Non-analytic Vector Fields with Constant Angular Speed", abstract = "We investigate the planar quasi-septic non-analytic systems which have a center-focus equilibrium at the origin and whose angular speed is constant. The system could be changed into an analytic system by two transformations, with the help of computer algebra system MATHEMATICA, the conditions of uniform isochronous center are obtained.
", keywords = "Non-analytic, center–focus problem, Lyapunov constant, uniform isochronous center.", volume = "5", number = "12", pages = "1961-3", }