Article Contents
Article Contents

# Lower bounds for the topological entropy

• We establish lower bounds for the topological entropy expressed in terms of the exponential growth rate of $k$-volumes. This approach provides the sharpest possible bounds when no further geometric information is available. In particular, our methods apply to (partially) volume-expanding dynamics with not necessarily compact phase space, including a large class of geodesic flows. As an application, we conclude that the topological entropy of these systems is positive.
Mathematics Subject Classification: 37C45, 37D40.

 Citation: