Classifications of germs of diffeomorphisms and fractal properties of their orbits – Maja Resman (University of Zagreb)


Sala Conferenze (Puteano, Centro De Giorgi).


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)->(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).

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