Amadeu Delshams, J. Tomas Lazaro
Pseudo-normal form near saddle-center or saddle-focus equilibria
(350K, Postscript)

ABSTRACT.  In this paper we introduce the pseudo-normal form, which 
generalizes the notion of normal form around an equilibrium. Its 
convergence is proved for a general analytic system in a 
neighborhood of a saddle-center or a saddle-focus equilibrium 
point. If the system is Hamiltonian or reversible, this 
pseudo-normal form coincides with the Birkhoff normal form, so we 
present a new proof in these celebrated cases. From the 
convergence of the pseudo-normal form for a general analytic system 
several dynamical consequences are derived, like the existence of 
local invariant objects.