Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation

# One resonant biholomorphisms and applications to quasi-parabolic germs

speaker: Filippo Bracci (Università di Roma 'Tor Vergata')

abstract: A one-resonant holomorphic diffeomorphism is a germ fixing the origin in Cn and whose differential at O has only a one-dimensional family of resonances plus some other finite resonances. In this talk I present a very recent work with D. Zaitsev where we describe normal forms and invariants for those diffeos. Starting from those, we prove existence of basins of attraction. Such basins are modelled over petals for the action of the map on the space of a particular foliation. As an application, we are able to show that (in the direction tangent to the eigenspace of 1) a quasi-parabolic germ either has a curve of fixed points, or has petals, or has basins of attraction, providing thus a complete picture of the local dynamics in this case.

timetable:
Mon 12 Oct, 10:20 - 11:20, Aula Dini
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