| On Two Noteworthy Deformations Of Negatively (2007) | |||||||||||||||
Abstract | |||||||||||||||
| Let M be a closed connected C Riemannian manifold whose geodesic flow OE is Anosov. Let ` be a smooth 1-form on M . Given 2 R small, let hEL () be the topological entropy of the Euler-Lagrange flow of the Lagrangian 1 x \Gamma ` x (v); and let hF () be the topological entropy of the geodesic flow of the Finsler metric, F (x; v) = jvj x \Gamma ` x (v): We show that where Var(`) is the variance of ` and h is the topological entropy of OE. We derive various consequences from this formula. | |||||||||||||||
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