doi:
10.3934/dcds.2005.12.555 
Full text:
(232.6K)
Katrin Gelfert -
Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal (email)
Abstract:
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.
Keywords: Topological entropy, Hausdorff dimension, geodesic flow.
Mathematics Subject Classification: 37C45, 37D40.
Received: October 2003
Revised:
August 2004
Published: December 2004
