seminar: Non existence of convergent normal form for general germs of unipotent diffeomorphisms

speaker: Javier Ribon (Universidade Federal Fluminense)

abstract: There exists a fruitful theory of normal forms applied to vector fields and diffeomorphisms. For instance given a germ of diffeomorphism the existence of a convergent normal form (i.e. a diffeomorphism embedded in a flow, belonging to the same class of formal conjugation) has dynamical implications (summability and resurgence properties, classification purposes...).

We prove that there exists a unipotent germ of complex analytic diffeomorphism with no convergent normal form in every dimension greater than 1. Such a property is for our example of geometrical type. The focus of this talk is not only on proving divergence but also on introducing some methods to do this task with as few calculations as possible.

timetable:
Wed 24 Jan, 12:20 - 13:20, Aula Dini
documents:

Ribon.pdf

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