TITLE:
Nekhoroshev theory and discrete averaging

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 the Nekhoroshev theorem for quasi-integrable
symplectic maps. In contrast to the classical methods, our proof is based on
the discrete averaging method and does not rely on transformations to normal
forms. At the centre of our arguments lies the theorem on embedding of a
near-the-identity symplectic map into an autonomous Hamiltonian flow with
exponentially small error.