Abstract:
The main focus of this project is to investigate which entropy related dynamical phenomena of geodesic flows on surfaces are geometric in nature and which are symplectic. For example, which phenomena generalize to three-dimensional Reeb flows? In three subprojects we will further develop the connection between finite energy foliations and symbolic dynamics to understand orbit travel, also in the context of the restricted three-body problem, and use chord contact homology to study measures of maximal entropy. Questions about non-finite energy holomorphic curves, so-called feral curves, will also be studied.