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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

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✦ 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.


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