Lower bounds for the topological entropy

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April 2005, 12(3): 555-565. doi: 10.3934/dcds.2005.12.555

Lower bounds for the topological entropy

1.	Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal

Received October 2003 Revised August 2004 Published December 2004

Abstract
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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: Hausdorff dimension, geodesic flow., Topological entropy.

Mathematics Subject Classification: 37C45, 37D4.

Citation: Katrin Gelfert. Lower bounds for the topological entropy. Discrete & Continuous Dynamical Systems - A, 2005, 12 (3) : 555-565. doi: 10.3934/dcds.2005.12.555

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