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
B2: Minimal geodesics
Knieper, Kunze
Abstract:
This project investigates minimal geodesics on complete Riemannian manifolds with non-compact universal cover, in particular their ergodic properties w.r.t. naturally defined invariant measures. We shall also deal with twist maps featuring non-periodic angles, which exclude the application of KAM theory or Aubry-Mather theory. However, the dynamics of the minimizing orbits are deeply connected to those described in classic results of Hedlund for the 2-torus. Hence we plan to transfer the techniques from the non-periodic angles setting to establish structural phenomena of minimal geodesics (like recurrence) on non-compact cylinders, for instance.
Group:
 
Prof. Gerhard Knieper (PI)
mail: gerhard.knieper at rub.de
phone: 0234 / 322 2381
room: NA 5/33
Faculty of Mathematics
Ruhr-University Bochum
Prof. Markus Kunze (PI)
mail: mkunze at math.uni-koeln.de
phone: 0221 / 470 7075
room: 129
Mathematical Institute
University of Cologne
Impressum Institution of DFG, MI University of Cologne and FM Ruhr-University Bochum