Starts 1 Feb 2016 17:00
Ends 1 Feb 2016 17:50
Central European Time
ICTP
Leonardo Building - Luigi Stasi Seminar Room
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.