On good approximations and Bowen-Series expansion

Abstract

We consider the continued fraction expansion of real numbers under the action of a non-uniform lattice in PSL(2,R) and prove metric relations between the convergents and a natural geometric notion of good approximations.

13 pages, 4 figures. Minor changes in the exposition. The content of this note was initially part of the preprint arXiv:1812.11921. Because of editorial reasons, the proof of main Theorem 3.1 in this note has been removed from arXiv:1812.11921. This material appears now separately under the title "On good approximations and Bowen-Series expansion"