Cubic Systems and Abel Equations

Journal of Differential Equations

Volumn 147, Issue 2, 1998, Pages 435-454

  Devlin, J ^a   Lloyd, N G ^a   Pearson, J M ^a  

^a ABERYSTWYTH UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000829449     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1998.3420     Document Type: Article

References (20)

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2. Alwash M. A. M., Lloyd N. G. Periodic solutions of a quartic non-autonomous equation. Nonlinear Anal. 11:1987;809-820.
3. M. Briskin, J. P. Françoise, Y. Yomdin, Centre conditions, compositions of polynomials and moments on algebraic curves, 1997.
4. Blows T. R., Lloyd N. G. The number of limit cycles of certain polynomial differential equations. Proc. Roy. Soc. Edinburgh Sect. A. 98:1984;215-239.
5. Christopher C. J., Devlin J. Isochronous centres in planar polynomial systems. SIAM J. Math. Anal. 28:1997;162-177.
6. Christopher C. J., Lloyd N. G., Pearson J. M. On Cherka's method for centre conditions. Nonlinear World. 2:1995;459-469.
7. Devlin J. Word problems related to the periodic solutions of non-autonomous systems. Math. Proc. Cambridge Philos. Soc. 108:1990;127-151.
8. J. Devlin, Cyclicity of critical points and the inverse Poincaré map, University of Wales, Aberystwyth, 1997.
9. Gasull A., Prohens R. Quadratic and cubic systems with degenerate infinity. J. Math. Anal. Appl. 198:1996;25-34.
10. Lloyd N. G. Small amplitude limit cycles of polynomial differential equations. Ordinary Differential Equations and Operators. Lecture Notes in Math. 1032:1982;Springer-Verlag, Berlin/New York. p. 357-364.
11. Lloyd N. G., Christopher C. J., Devlin J., Pearson J. M., Yasmin N. Quadratic-like cubic systems. Differential Equations Dynam. Systems. 5:1997;329-345.
12. Lloyd N. G., Pearson J. M. REDUCE and the bifurcation of limit cycles. J. Symbolic Comput. 9:1990;215-224.
13. Lloyd N. G., Pearson J. M. Five limit cycles for a simple cubic system. Publ. Math. 41:1997;199-208.
14. Lloyd N. G., Pearson J. M., Romanovsky V. G. Computing integrability conditions for a cubic differential system. Comput. Math. Appl. 32:1996;99-107.
15. N. G. Lloyd, J. M. Pearson, V. A. Romanovsky, Centre conditions for cubic systems, University of Wales, Aberystwyth, 1997.
16. Lloyd N. G., Pearson J. M., Saez E., Szanto I. Limit cycles of a cubic Kolmogorov system. Appl. Math. Lett. 9:1996;15-18.
17. Pearson J. M. Hilbert's Sixteenth Problem: An Approach Using Computer Algebra. 1992;University of Wales, Aberystwyth.
18. Pearson J. M., Lloyd N. G., Christopher C. J. Algorithmic derivation of centre conditions. SIAM Rev. 38:1996;619-636.
19. Pleshkan I. I. A new method of investigating the isochronicity of a system of two differential equations. Differentisial'nye Uravneniya. 5:1968;796-802.
20. Pleshkan I. I. Isochronicity conditions for systems of two differential equations. Differential 'nye Uravneniya. 4:1968;1991-1993.