ICTP Mathematics Seminar - Thursday 2 May 2013, at 15:00

[Mabilo]

M A T H E M A T I C S   S E M I N A R S   2013

Thursday, 2 May, at 15.00 hrs.

Cristina Lizana Araneda
(PUC, Rio de Janeiro, Brazil)

"Robust Transitivity for Endomorphisms"


Abstract:
We address the problem of the conditions under which an 
endomorphism(non-invertible map) having a dense orbit ensures that a 
sufficiently close perturbed map also exhibits a dense orbit.
In this context, we give sufficient conditions, which cover a large 
class of examples, for endomorphisms on the n-dimensional torus to be 
robustly transitive: the endomorphism must be volume expanding and any 
large connected arc must contain a point such that its future orbit 
belongs to an expanding region.
(Joint work with E. Pujals)

If we have enough time, I will show some ergodic properties for a 
generic subset of  this class of maps. More concretely, the existence of 
interesting measures such as ergodic expanding invariant measures with 
full support and exhibiting exponential decay of correlations.
(Joint work with V. Pinheiro and P.Varandas)

Some examples will be shown.

Venue: Luigi Stasi Seminar Room, first floor , Leonardo Building