Hyperbolic dynamics of Euler-Lagrange flows on prescribed energy levels
Real analytic convex surfaces with positive topological entropy and rigid body dynamics.
Topological pressure for geodesic flows
On Anosov energy levels of convex Hamiltonian systems.
Collective geodesic flows
We show that most compact semi-simple Lie groups carry many left invariant metrics with positive topological entropy. We also show that many homogeneous spaces admit collective Riemannian metrics arbitrarily close to the bi-invariant metric and whose geodesic flow has positive topological entropy. Other properties of collective geodesic flows are also discussed.
Stability is not open
We give an example of a symplectic manifold with a stable hypersurface such that nearby hypersurfaces are typically unstable.
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