Horocycle flow on negative variable curvature surface is standard
Dynamical Systems
2018-10-19 v1
Abstract
We provide a new proof that the horocycle flow preserving the Margulis measure on a variable negative curvature surface is standard. This was first proved by Ratner. The main purpose of this note is to provide a simplified case of the arguments for Kakutani equivalence of unipotent flows on homogeneous spaces, which have similar but more complicated structures, as well as illustrate the versatility of the method by applying it to a non-homogeneous flow.
Cite
@article{arxiv.1810.07755,
title = {Horocycle flow on negative variable curvature surface is standard},
author = {Adam Kanigowski and Kurt Vinhage and Daren Wei},
journal= {arXiv preprint arXiv:1810.07755},
year = {2018}
}