  Topological entropy is not lower semi-continous: small perturbation of the
dynamical system can lead to a collapse of entropy. In this note we show that
for some special classes of dynamical systems (geodesic flows, Reeb flows,
positive contactomorphisms) topological entropy at least is stable in the sense
that there exists a nontrivial continuous lower bound, given that a certain
homological invariant grows exponentially.
