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.
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Viernes 17/6 a las 14:30, Salón de seminarios del IMERL
Contacto: León Carvajales - lcarvajales [at] cmat.edu.uy