Pasar al contenido principal

Unique ergodicity of the horocyclic flow of certain surfaces without conjugate points

Fecha de inicio:

Seminario de Sistemas Dinámicos

Título: "Unique ergodicity of the horocyclic flow of certain surfaces without conjugate points."

Expositor: Sergi Burniol (IMJ-PRG)

Resumen:
 
There are strong connections between the dynamics of the   geodesic flow and the
horocyclic flow defined on the unit tangent   bundle of certain Riemannian
surfaces.

Furstenberg and Marcus proved in the 70s that the horocyclic flow of a
negatively curved compact surface is uniquely ergodic, i.e. it admits   a unique
invariant probability measure. I will explain why this result   still holds for
a compact surface without conjugate points, genus   greater than 1 and
continuous Green bundles. The proof uses the   construction of the measure of
maximal entropy for the geodesic flow   in a recent paper of Climenhaga-Knieper-
War, and the semiconjugation   of the geodesic flow with an expansive continuous
flow with local   product structure, established by Gelfert-Ruggiero.
--------------------------------------------------------------------------------
Viernes 17/6 a las 14:30, Salón de seminarios del IMERL

Contacto: León Carvajales - lcarvajales@cmat.edu.uy

 

Instituto o Unidad
Fecha de fin