Starshaped polytopes exist in R^4 such that every starshaped smoothing of their boundary induces a Reeb flow with positive topological entropy, answering Ostrover-Ginzburg; analogous C^0 metrics on surfaces have geodesic flows with h_top > C for any smoothing.
Opshtein.C 0-rigidity of characteristics in symplectic geometry.Ann
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Polytopes and $C^0$-Riemannian metrics with positive $h_{\rm top}$
Starshaped polytopes exist in R^4 such that every starshaped smoothing of their boundary induces a Reeb flow with positive topological entropy, answering Ostrover-Ginzburg; analogous C^0 metrics on surfaces have geodesic flows with h_top > C for any smoothing.