Polynomial Lienard equations near infinity

We study the behaviour near infinity of the (generalized) Lienard equations (x) over dot = y, (y) over dot = -Sigma(k=0)(m) a(k)x(k) - y Sigma(k=0)(n) b(k)x(k) providing a complete classification using Poincare compactificati on as well as Poincare-Lyapunov compactification. We show that all the nece ssary information is contained in a(m) and b(n), except for the so called " center-focus" problem occuring in case m greater than or equal to 2n + 1 wi th m, n odd, and where the behaviour also depends on the value of the other coefficients a(i) and b(j). We also indicate how to take care about obtain ing uniform information near infinity. (C) 1999 Academic Press.