Symplectic Structures in Geometry, Algebra and Dynamics
Collaborative Research Centre TRR 191
 
A1, A2, A3, A5, A6, A7
B1, B2, B3, B4, B5, B6, B7
C1, C2, C3, C4, C5
Dynamics & Variational Methods
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.
Group:
 
Prof. Barney Bramham (PI)
mail: barney.bramham at rub.de
phone: 0234 / 322 4179
room: NA 5/32
Faculty of Mathematics
Ruhr-University Bochum
Prof. Gerhard Knieper (PI)
mail: gerhard.knieper at rub.de
phone: 0234 / 322 2381
room: NA 5/33
Faculty of Mathematics
Ruhr-University Bochum
Impressum Institution of DFG, MI University of Cologne and FM Ruhr-University Bochum