Polynomial Liénard Equations near Infinity

✍ Scribed by Freddy Dumortier; Chris Herssens

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 378 KB
• Volume: 153
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1998.3543

✦ Synopsis

We study the behaviour near infinity of the (generalized) Lie nard equations x* = y, y* =& m k=0 a k x k & y n k=0 b k x k providing a complete classification using Poincare compactification as well as Poincare Lyapunov compactification. We show that all the necessary information is contained in a m and b n , except for the so called ``center-focus'' problem occuring in case m 2n+1 with 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 obtaining uniform information near infinity.