Self-intersecting Geodesics and Entropy of the Geodesic Flow
نویسندگان
چکیده
Our main observation concerns closed geodesics on surfaces M with a smooth Finsler metric, i.e. a function F : TM → [0,∞) which is a norm on each tangent space TpM , p ∈ M , which is smooth outside of the zero section in TM , and which is strictly convex in the sense that Hess(F ) is positive definite on TpM \ {0}. One calls a Finsler metric F symmetric if F (p,−v) = F (p, v) for all v ∈ TpM . We denote the universal cover of a surface M by M̂ . Any Finsler metric on M lifts to a Finsler metric on M̂ which we again denote by F
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