An example of how the Ricci Flow can increase topological entropy

Details An example of how the Ricci Flow can increase topological entropy An example of how the Ricci Flow can increase topological entropy

2006-09-22

arxiv.org/abs/math/0609642v1

Mathematics

Dynamical Systems

15 pages, 4 figures

Scientific paper

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.

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