Lower bounds for the topological entropy

Katrin Gelfert

doi:10.3934/dcds.2005.12.555

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2005, Volume 12, Issue 3: 555-565. Doi: 10.3934/dcds.2005.12.555

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Lower bounds for the topological entropy

Katrin Gelfert^1,

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

Received: September 30, 2003

Revised: July 31, 2004

Published: March 2005

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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.

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Mathematics Subject Classification: 37C45, 37D40.

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