An example of how the Ricci Flow can increase topological entropy

2006/09/22 by Dan Jane, Jane, Dan · 1 citation
Mathematics · Medicine · Physics and Astronomy · #34C35 #53C44 #Advanced Mathematical Theories and Applications #Biofield Effects and Biophysics #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/0609642

openalex publication_date 2006/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Monotonicity of topological entropy along the Ricci flow near a hyperbolic metric

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