Some of the dynamical properties of the geodesic flow $\phi$ of a closed Riemannian manifold $M$ are independent of the metric on $M$. For "most" manifolds $M$, one can detect a strong instability of the dynamics of $\phi$, notably through the positivity of the exponential growth rate of the number of closed orbits or through the positivity of the topological entropy of $\phi$. These classical results considerably generalize to the world of symplectic and contact geometry. I will give an overview on the relevant results in this direction. Also I will present a joint construction with Alves of contact structures on spheres such that all its Reeb flows have positive topological entropy. If time permits I explain how the exponential growth of Rabinowitz Floer homology, besides providing new interesting examples of contact manifolds that only carry Reeb flows with positive entropy, has applications to the dynamics of geodesic flows.
Dienstag, den 11. Dezember 2018 um 13.00 Uhr, in Mathematicon, INF 205, SR C Dienstag, den 11. Dezember 2018 at 13.00, in Mathematicon, INF 205, SR C
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Peter Albers