15 oct 2015 -- 15:00
Sala Conferenze, Collegio Puteano, Pisa
Seminari di Sistemi Dinamici, Pisa
Abstract.
We are motivated by the question of recognizing a germ of a diffeomorphism by looking at only one (discrete) orbit. The method we propose uses fractal properties of the orbit: its box dimension, or, more generally, the area of its epsilon-neighborhood or appropriate generalizations. For parabolic germs $f:(C,0)\to(C,0)$, we study properties of this area function, as function of parameter epsilon and also of the initial point. We address formal and analytic classification of germs. Furthermore, in a work in progress, the same method is proposed for recognizing real germs with Dulac-type expansions. As a prerequisite, a formal normal form result (of independent interest) for Dulac germs is given in a class of power-log transseries (a joint work with P. Mardesic, J.P. Rolin and V. Zupanovic).