The return sequence of the Bowen-Series map for punctured surfaces

• Autorzy: Manuel Stadlbauer
• Języki publikacji: EN

Abstrakty

EN

For a non-compact hyperbolic surface M of finite area, we study a certain Poincaré section for the geodesic flow. The canonical, non-invertible factor of the first return map to this section is shown to be pointwise dual ergodic with return sequence (aₙ) given by
aₙ = π/(4(Area(M) + 2π)) · n/(log n).
We use this result to deduce that the section map itself is rationally ergodic, and that the geodesic flow associated to M is ergodic with respect to the Liouville measure.

Kategorie tematyczne

• 30F35: Fuchsian groups and automorphic functions
• 51M15: Geometric constructions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 182
• Numer: 3
• Strony: 221-240

Daty

wydano

2004

Twórcy

autor

Manuel Stadlbauer

• Institut für Mathematische Stochastik, Maschmühlenweg 8-10, 37073 Göttingen, Germany

Identyfikatory

DOI

10.4064/fm182-3-3