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N.N. BAUTIN, ‘On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or centre type', Mat. Sb.N.S. 30 (72) (1952) 181–196 (in Russian); Amer. Math. Soc. Transl. No.100 (1954), and in Amer. Math. Soc. Transl. (1) 5 (1962) 396–413.
T. BLOWS and N.G. LLOYD, ‘On the number of limit cycles of quadratic systems', preprint.
T. BLOWS and N.G. LLOYD, ‘The number of limit cycles of certain cubic differential systems', preprint.
W.A. COPPEL, ‘A survey of quadratic systems', J. Differential Equations 2 (1966) 293–304.
F. GRÖBBER and K.-D. WILLAMOWSKI, ‘Liapunov approach to multiple Hopf bifurcation', J. Math. Anal. Appl. 71 (1979) 333–350.
N.G. LLOYD, ‘The number of periodic solutions of the equation ż = zN + p1(t)zN-1+...+pN(t)', Proc. London Math. Soc. (3) 27 (1973) 667–700.
N.G. LLOYD, ‘On analytic differential equations', Proc. London Math. Soc. (3) 30 (1975) 430–444.
N.G. LLOYD, ‘On a class of differential equations of Riccati type', J. London Math. Soc. (2) 10 (1975) 1–10.
V.V. NEMYTSKII and V.V. STEPANOV, Qualitative theory of differential equations (Princeton University Press, 1960).
A.L. NETO, ‘On the number of solutions of the equation \(dx{\mathbf{ }}/{\mathbf{ }}dt = \sum\limits_{j = 0}^n {a_j (t)x^j ,0 \leqslant t \leqslant 1}\), for which x(0) = x(1)', Invent. Math. 59 (1980) 67–76.
I.G. PETROVSKII and E.M. LANDIS, ‘On the number of limit cycles of the equation dy/dx = P(x,y)/Q(x,y), where P and Q are polynomials of the second degree', Mat. Sb.N.S. 37 (79) (1955), 209–250 (in Russian); Amer. Math. Soc. Transl. (2) 10 (1958) 177–221.
I.G. PETROVSKII and E.M. LANDIS, ‘On the number of limit cycles of the equation dy/dx = P(x,y)/Q(x,y), where P and Q are polynomials, Mat. Sb.N.S. 43 (85) (1957) 149–168 (in Russian); Amer. Math. Soc. Transl. (2) 14 (1960) 181–200.
I.G. PETROVSKII and E.M. LANDIS, ‘Corrections to the articles "On the number of limit cycles of the equations dy/dx = P(x,y)/Q(x,y) where P and Q are polynomials of the second degree" and "On the number of limit cycles of the equation dy/dx = P(x,y)/Q(x,y) where P and Q are polynomials"', Mat. Sb.N.S. 48 (90) (1959) 253–255 (in Russian).
QIN YUANXUN, SHI SONGLING and CAI SUILIN, ‘On limit cycles of planar quadratic systems', Sci. Sinica 25 (1982) 41–50.
SHI SONGLING, ‘A concrete example of the existence of four limit cycles for plane quadratic systems', Sci. Sinica 23 (1980) 153–158.
SHI SONGLING, ‘A method of constructing cycles without contact around a weak focus', J. Differential Equations 41 (1981) 301–312.
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© 1983 Springer-Verlag
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Lloyd, N.G. (1983). Small amplitude limit cycles of polynomial differential equations. In: Everitt, W.N., Lewis, R.T. (eds) Ordinary Differential Equations and Operators. Lecture Notes in Mathematics, vol 1032. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076806
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DOI: https://doi.org/10.1007/BFb0076806
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