An example of how the Ricci Flow can increase topological entropy
Dynamical Systems
2007-05-23 v1 Differential Geometry
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.
Cite
@article{arxiv.math/0609642,
title = {An example of how the Ricci Flow can increase topological entropy},
author = {Dan Jane},
journal= {arXiv preprint arXiv:math/0609642},
year = {2007}
}
Comments
15 pages, 4 figures