Abstract
We show that the set of C∞ Riemannian metrics on S2 or ℝP2 whose geodesic flow has positive topological entropy is open and dense in the C2 topology. The proof is partially based on an analogue of Franks' lemma for geodesic flows on surfaces.
Citation
Gonzalo Contreras-Barandiarán. Gabriel P. Paternain. "Genericity of Geodesic Flows with Positive Topological Entropy on S2." J. Differential Geom. 61 (1) 1 - 49, May, 2002. https://doi.org/10.4310/jdg/1090351319
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