R. Mao et D. Wang, JUMPING PROPERTY OF LYAPUNOV VALUES, Science in China. Series A, Mathematics, Physics, Astronomy & Technological Sciences, 39(12), 1996, pp. 1280-1287
A sufficient condition for kth Lyapunov value to be zero for planar po
lynomial vector fields is given, which extends the result of ''jumping
property'' of Lyapunov values obtained by Wang Duo to more general ca
ses. A concrete example that the origin cannot be weak focus of order
1, 2, 4, 5, 8 is presented.