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

Manuel Stadlbauer. "The return sequence of the Bowen-Series map for punctured surfaces." Fundamenta Mathematicae 182.3 (2004): 221-240. <http://eudml.org/doc/283397>.

@article{ManuelStadlbauer2004,
abstract = { 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. },
author = {Manuel Stadlbauer},
journal = {Fundamenta Mathematicae},
keywords = {geodesic flow; return map; pointwise dual ergodicity},
language = {eng},
number = {3},
pages = {221-240},
title = {The return sequence of the Bowen-Series map for punctured surfaces},
url = {http://eudml.org/doc/283397},
volume = {182},
year = {2004},
}

TY - JOUR
AU - Manuel Stadlbauer
TI - The return sequence of the Bowen-Series map for punctured surfaces
JO - Fundamenta Mathematicae
PY - 2004
VL - 182
IS - 3
SP - 221
EP - 240
AB - 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.
LA - eng
KW - geodesic flow; return map; pointwise dual ergodicity
UR - http://eudml.org/doc/283397
ER -