Geodesic flow, connecting orbits and almost full foliation
Considering the geodesic flow of the torus \(\mathbb{T}^2\), endowed with a metric which is a certain local deformation of the flat one, the authors exhibit an example for which the following special complicated dynamical behaviour holds: \(\bullet\) the set of minimal geodesics having a given average slope can have Hausdorff dimension 2 (in the unit tangent bundle); \(\bullet\) any two minimal sets with different rational slopes can be connected by some orbit.
scientific article; zbMATH DE number 5133946
scientific article