ICTP Mathematics Seminars - Two seminars on Monday 1 February from 16:00

[Math Section]

M A T H E M A T I C S   S E M I N A R S   2016


1) Monday, 1 February, 16:00 - 16:50 hrs.


Paulo Brandao (IMPA)


Topological attractors for Contracting Lorenz Maps

Abstract:
We show that contracting Lorenz maps with negative Schwarzian derivative 
have only one topological attractor.
More precisely, if such a map f has no finite attractor (periodic 
attractors or super-attractors), then there is a transitive compact set 
Λ such that it is the omega-limit for a residual set of the interval.
 From the techniques developed to get this we also have a Spectral
Decomposition Theory for these Lorenz maps.





2) Monday, 1 February, 17:00 - 17:50 hrs.


Vilton Pinheiro (UFBA)

Expanding Lorenz maps with abundance of invariant ergodic probabilities 
having +∞ as Lyapunov exponent

Abstract:

We show that there are Cr Lorenz maps f : [−1, 1] \ {0} → [−1, 1], r ≥ 
2, with uncountable many ergodic invariant probabilities μ with positive 
entropy, infinite Lyapunov exponent, full support (suppμ = [−1, 1]) and 
fast recurrence to the singularity. Such measures make more difficult 
the study of the Thermodynamical Formalism for the expanding Lorenz 
maps. On the other hand, we also give a generic condition for a Lorenz 
map to present only invariant probabilities with finite Lyapunov 
exponent and slow recurrence to the singularity. We also discuss the 
Thermodynamical Formalism for both cases.





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