Exponential mixing of the Teichmüller flow on affine invariant manifolds

Abstract

Let S be a non-exceptional oriented surface of finite type. We give a new proof based on symbolic coding of the following result of Avila and Gouezel. The Teichmueller flow is exponentially mixing with respect to any ergodic SL(2,R)-invariant Borel probability measure.

28p; the main result is due to Avila and Gouezel. Some details were added, minor edits. This is the third rewritten and extended part of arXiv:1112.6197, which was split into four parts. arXiv admin note: text overlap with arXiv:1112.6107