---------------------------- Original Message ---------------------------- Subject: Ciclo "Baby geometri" - promemoria dei seminari di Jasmin e Fabrizio From: "simone calamai" simocala@gmail.com Date: Mon, May 6, 2013 9:54 am --------------------------------------------------------------------------

Ciao a tutti, vi ricordiamo che domani Martedi' 7 Maggio ci saranno due seminari

del ciclo "Baby geometri"; il primo seminario sara'

- alle ore 16:00, in Sala Seminari - speaker: Jasmin Raissy (Univ. de Toulouse) - Titolo: Normal forms in local holomorphic dynamics - Abstract: Normal forms are a very important tool in several branches of mathematics. I shall discuss the normalization and the linearization problems for germs of biholomorphism of several complex variables with an isolated fixed point, starting from the classical Poincare'-Dulac procedure, and then focusing on the case of multi-resonant biholomorphisms, i.e., such that the resonances among the eigenvalues of the differential are generated over N by a finite number of linearly independent multi-indices. I shall give sharp conditions for the existence of basins of attraction where a Fatou coordinate can be defined, and we shall obtain a generalization of the Leau-Fatou flower theorem, providing a complete description of the dynamics in a full neighborhood of the fixed point for 1-resonant parabolically attracting holomorphic germs in Poincare'-Dulac normal form. If time allows I will also explain more recent results on 2-resonant germs.

e il secondo seminario sara'

- alle ore 17:30, in Sala Seminari - speaker: Fabrizio Bianchi (SNS di Pisa) - Titolo: Dynamics of holomorphic homogeneous vector fields in C^n through Poincare'-Bendixson theorems on (something like) P^{n-1}(C) - Abstract: The topic of this talk will concern the study of the dynamics of endomorphisms of *C*^n tangent to the identity, i.e. with differential equal to the identity. An important class (which is conjectured to be a model for generic germs of endomorphisms tangent to the identity) of maps of this type is the one of the maps at time one of holomorphic homogeneous vector fields, for which it is possible to study the integral curves of the field to obtain information on the behavior of orbits of the original system. Furthermore, in *[1]* Abate and Tovena showed, using results from *[2]*, that there exists a correspondence between these integral curves and the geodesics on *P*^{n−1} (*C*), the blow-up of the origin, for a suitable meromorphic connection along a foliation in Riemann surfaces, whose poles coincide with the invariant directions for the homogeneous field. Using Poincaré-Bendixson-type theorems for the geodesics of these connections it is possible to study the integral curves for the field, and so the dynamics of the starting endomorphism.

(Tra il primo e il secondo seminario, sara' offerta una merenda)