Topology & Equivariant Theories 
A1, A2, A3, A5, A6, A7

Dynamics & Variational Methods 
B1, B2, B3, B4, B5, B6, B7

Algebra, Combinatorics & Optimization 
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 lowdimensional Hamiltonian systems, notably the geodesic flows on the 2sphere and the 2torus, and their generalizations to Reeb flows on the 3sphere and the 3torus. For example, using finite energy foliations we would like to prove that Reeb flows on the 3sphere with a dense orbit and at least three periodic orbits must have positive topological entropy. For lowdimensional 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  RuhrUniversity Bochum 
  Prof. Gerhard Knieper (PI)  mail: gerhard.knieper at rub.de  phone: 0234 / 322 2381  room: NA 5/33  Faculty of Mathematics  RuhrUniversity Bochum 


