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

Debido a la ocupación de la Facultad de Ingeniería decretada por el Centro de estudiantes, el seminario de sistemas dinámicos del día de hoy queda SUSPENDIDO.

La charla de Sylvain Crovisier pasa para el lunes 7 de setiembre, lugar y hora a confirmar.

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.