New results on noncompact harmonic manifolds (2009)
The Lichnerowicz conjecture asserts that all harmonic manifolds are either flat or locally symmetric spaces of rank~1. This conjecture has been proved by Z. Szab\'{o} \cite{Sz} for harmonic manifolds...
Near action-degenerate periodic-orbit bunches: A skeleton of chaos (2009)
Altland, Alexander, Braun, Petr, Haake, Fritz, Heusler, Stefan, Knieper, Gerhard, Müller, Sebastian
Long periodic orbits of hyperbolic dynamics do not exist as independent individuals but rather come in closely packed bunches. Under weak resolution a bunch looks like a single orbit in configuration...
C ∞ genericity of positive topological entropy for geodesic flows (2009)
We show that there is a C ∞ open and dense set of positively curved metrics on S 2 whose geodesic flow has positive topological entropy, and thus exhibits chaotic behavior. The geodesic flow for...
C ∞ genericity of positive topological entropy for geodesic flows (2008)
We show that there is a C ∞ open and dense set of positively curved metrics on S 2 whose geodesic flow has positive topological entropy, and thus exhibits chaotic behavior. The geodesic flow for...
C∞ Genericity of Positive Topological Entropy for Geodesic Flows on S2 (2002)
Knieper, Gerhard, Weiss, Howard
We show that there is a C∞ open and dense set of positively curved metrics on S2 whose geodesic flow has positive topological entropy, and thus exhibits chaotic behavior. The geodesic flow for each...