Real analytic convex surfaces with positive topological entropy and rigid body dynamics (Q1313502)

The author exhibits explicit real analytic metrics on \(S^ 2\) and \(\mathbb{R} P^ 2\) with positive curvature and positive topological entropy. These metrics are constructed from the Euler Poisson flows which describe the motion of a rigid body on axially symmetric face fields. It is shown that for specific force fields the flow possesses a horseshoe and hence positive topological entropy. Via the Maupertuis principle these flows give rise to convex metrics on \(S^ 2\) with positive topological entropy.