Periodic orbits in complex Abel equations
Tài liệu tham khảo
Alwash, 1987, Nonautonomous equations related to polynomial two-dimensional systems, Proc. Roy. Soc. Edinburgh Sect. A, 105, 129, 10.1017/S0308210500021971
Andersen, 1999, Existence of closed solutions of an equation x˙=f(t,x), where fx′(t,x) is weakly convex or concave in x, J. Math. Anal. Appl., 229, 480, 10.1006/jmaa.1998.6171
Andronov, 1973
Brickman, 1977, Conformal equivalence of analytic flows, J. Differential Equations, 25, 310, 10.1016/0022-0396(77)90047-X
Briskin, 1999, Center conditions, compositions of polynomials and moments on algebraic curves, Ergodic Theory Dynam. Systems, 19, 1201, 10.1017/S0143385799141737
Carbonell, 1988, Limit cycles of a class of polynomial systems, Proc. Roy. Soc. Edinburgh Sect. A, 109, 187, 10.1017/S0308210500026755
Cherkas, 1976, Number of limit cycles of an autonomous second-order system, Differ. Equ., 5, 666
Devlin, 1998, Cubic systems and Abel equations, J. Differential Equations, 147, 435, 10.1006/jdeq.1998.3420
A. Gasull, A. Guillamon, Limit cycles for generalized Abel equations, Internat. J. Bifur. Chaos Appl. Sci. Engrg., in press
Gasull, 1990, Limit cycles for a class of Abel equations, SIAM J. Math. Anal., 21, 1235, 10.1137/0521068
Il'yashenko, 2000, Hilbert-type numbers for Abel equations, growth and zeros of holomorphic functions, Nonlinearity, 13, 1337, 10.1088/0951-7715/13/4/319
Il'yashenko, 2004, Selected topics in differential equations with real and complex time, vol. 137, 317
Lins Neto, 1980, On the number of solutions of the equation dx/dt=∑j=0naj(t)xj, 0⩽t⩽1 for which x(0)=x(1), Invent. Math., 59, 67
Lloyd, 1973, The number of periodic solutions of the equation z˙=zN+p1(t)zN−1+⋯+pN(t), Proc. London Math. Soc., 27, 667, 10.1112/plms/s3-27.4.667
Lloyd, 1975, On a class of differential equations of Riccati type, J. London Math. Soc., 10, 1, 10.1112/jlms/s2-10.1.1
Lloyd, 1979, A note on the number of limit cycles in certain two-dimensional systems, J. London Math. Soc., 20, 277, 10.1112/jlms/s2-20.2.277
Panov, 1999, On the diversity of Poincaré mappings for cubic equations with variable coefficients, Funct. Anal. Appl., 33, 310, 10.1007/BF02467118
Pliss, 1966
Watson, 1944