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An example of how the Ricci flow can increase topological entropy

Published online by Cambridge University Press:  01 December 2007

DAN JANE
DAN JANE*
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK (email: jdtj2@cam.ac.uk)
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Abstract

We give a surface for which the Ricci flow applied to the metric will increase the topological entropy of the geodesic flow. Specifically, we first adapt the Melnikov method to apply to a Ricci flow perturbation and then we construct a surface which is closely related to a surface of revolution, but does not quite have rotational symmetry. This is done by adapting the Liouville metric representation of a surface of revolution. The final steps of the Melnikov method require numerical integration.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 6 , December 2007 , pp. 1919 - 1932
Copyright
Copyright © Cambridge University Press 2007

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