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

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.

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