A Finsler Geodesic Flow on $T^2$ With Positive Metric Entropy

Abstract

We use a theorem of P. Berger and D. Turaev to construct an example of a Finsler geodesic flow on the 2-torus with a transverse section, such that its Poincaré return map has positive metric entropy. The Finsler metric generating the flow can be chosen to be arbitrarily $C^{\infty }$-close to a flat metric.