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An example of how the Ricci Flow can increase topological entropy

Dan Jane
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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.

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Dan Jane. 2006-09-22. An example of how the Ricci Flow can increase topological entropy. https://arxiv.org/abs/math/0609642

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