We study an invariant of dynamical systems called naive entropy, which is defined for both measurable and topological actions of any countable group. We focus on nonamenable groups, in which case the invariant is two-valued, with every system having naive entropy either zero or infinity. Bowen has conjectured that when the acting group is sofic, zero naive entropy implies sofic entropy at most ...

We study the topological entropy of the magnetic flow on closed Riemannian surface. We prove that if the magnetic flow has a non-hyperbolic closed orbit in some energy set T c M = E −1 (c), then there exists an exact C ∞-perturbation of the 2-form Ω such that the new magnetic flow has positive topological entropy in T c M. We also prove that if the magnetic flow has an infinite number of closed...

We study the topological entropy of the magnetic flow on closed riemannian surface. We prove that if the magnetic flow has a non-hyperbolic closed orbit in some energy set T c M = E −1 (c), then there exists an exact C ∞-perturbation of the 2-form Ω such that the new magnetic flow has positive topological entropy in T c M. We also prove that if the magnetic flow has an infinite number of closed...