B1: Topological entropy and geodesic flows on surfaces

Bramham, Knieper

Abstract: The focus of this project is to investigate the relation of zero topological entropy and integrability for low-dimensional Hamiltonian systems, notably the geodesic flows on the 2-sphere and the 2-torus, and their generalizations to Reeb flows on the 3-sphere and the 3-torus. For example, using finite energy foliations we would like to prove that Reeb flows on the 3-sphere with a dense orbit and at least three periodic orbits must have positive topological entropy. For low-dimensional Hamiltonian systems with zero topological entropy we hope to show the existence of integrable approximations.