SEMINAIRE Mulhousien de
MATHEMATIQUES
résumé/abstract
Grisha Kolutsky
(Université d’Etat de Moscou Lomonossov)
On the Hilbert-Smale problem
In 1998 S. Smale suggested to consider a restriction of the second part of the 16th Hilbert problem to Lienard equations. In this talk we
will show how to get some explicit
upper estimates for the number
of limit cycles of (generalized) Lienard equations. There are two different parts of this work.
In the first part we deal with
some geometric properties of the phase space. The
second part is an application of the theorem of Ilyashenko and Yakovenko (that binds the number
of zeros and the growth of
a holomorphic function) to a
Poincaré map.
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Derniéres modifications / Last modifications : 29 novembre 2009