TITLE:
On exponentially accurate approximation of a near the identity map by an autonomous flow

AUTHORS:
Vassily Gelfreich^(1), Arturo Vieiro^(2,3),

(1) Mathematics Institute,
     University of Warwick, Coventry CV4 74 AK, UK
   
(2) Department de Matemàtiques i Informàtica,
    Universitat de Barcelona (UB), Barcelona, Spain.
(3) Centre de Recerca Matemàtica, Edifici C,
    Campus Bellaterra, 08193 Bellaterra, Spain.

ABSTRACT:

This paper contains a proof of a refined version of Neishtadt's theorem which
states that an analytic near-identity map can be approximated by the time-one
map of an autonomous flow with exponential accuracy. We provide explicit
expressions for the vector fields and give explicit bounds for the error terms.