FM 2005-6

Author: Guido Gentile

Title: Brjuno numbers and dynamical systems
 
Abstract: We shall consider some elementary analytic dynamical systems widely studied in literature, which are perturbations of integrable (linear) ones. A classical problem is to study the conditions for the perturbed system to be analytically conjugated to the linear one, that is the conditions for the existence of an analytic change of coordinates which maps the perturbed system to the linear one. We shall see that such conditions can be naturally expressed in terms of the Diophantine properties of a suitable parameter.

Keywords: Bryuno number; Bryuno function; Standard map; Semi-standard map; Siegel's problem; Conjugating function; Radius of convergence.

Guido Gentile
Dipartimento di Matematica
Università di Roma Tre
Largo San Leonardo Murialdo 1, 00146 Roma, Italy
e-mail: gentile@mat.uniroma3.it