Forthcoming Dynamical Systems seminar

[math]

M A T H E M A T I C S   S E M I N A R S   2011

- DYNAMICAL SYSTEMS -



Tuesday, 1 February, at 14:00 hrs.


Dr. Benito Pires
(University of Sao Paulo, Brazil)


"Closing perturbations for vector fields with nontrivial recurrent 
trajectories"

Abstract:
Let M be a closed 2-manifold and X be a C^r vector field on M.
We say that a trajectory of X is nontrivial if its not an equilibrium 
point nor a periodic trajectory. A trajectory of X is called recurrent 
if it accumulates on itself. The C1 closing lemma problem of Pugh states 
that a nontrivial recurrent trajectory can be made periodic by 
arbitrarily small perturbations of the vector field in the topology C^1. 
In this talk, we present a class of vector fields for which 
perturbations of the vector field in the topology C^2 make the 
nontrivial recurrent trajectory into a periodic trajectory. Joint work 
with Carlos Gutierrez.


VENUE: Luigi Stasi Seminar Room
(ICTP Leonardo da Vinci Building, first floor)