u-Gibbs measures of partially hyperbolic Anosov diffeomorphisms of T^3.

El seminario de sistemas dinámicos se realizará el martes 8 de
setiembre a las 14:30 en el salón 101.
Abajo encontrarán toda la información de la charla.
Aclaramos que los seminarios de profesores visitantes entran en el marco
de "actividades académicas impostergables" decretadas por la Udelar.

Resumen: It is well known that every transitive Anosov diffeomorphism
admits a unique physical measure: this measure is SRB, i.e. it is smooth
along the unstable leaves. Considering Anosov systems which also
preserve a sub-foliation by strong unstable leaves, one can similarly
consider u-Gibbs measures, i.e. measures whose conditional measures
along strong u-leaves are smooth. In this talk, we will discuss the
following question for Anosov diffeomorphisms of T^3: do u-Gibbs
measures necessarily coincide with the SRB measure? Under a generic
transversality assumption, this question was answered affirmatively by
Katz and independently by S. Alvarez, M. Leguil, D. Obata and B.
Santiago (ALOS). In a joint work in progress with A., L., O. and S., we
get a similar conclusion in the remaining case, that is when the stable
and the strong unstable foliations jointly integrate. Our approach
involves the construction of a
horocyclic flow on a suspended space.
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