Mathematics – Dynamical Systems
Scientific paper
2009-11-16
Mathematics
Dynamical Systems
Revised version, 5 pages. The previous version was incorrect due to the use of a misquoted result (which was also misstated in
Scientific paper
In 2004, Manning showed that the topological entropy of the geodesic flow for a surface of negative curvature decreases as the metric evolves under the normalised Ricci flow. It is an interesting open problem, also due to Manning, to determine to what extent such behaviour persists for higher dimensional manifolds. In this short note, we describe the problem and give a strong criterion under which monotonicity of the topological entropy can be established for a short time. In particular, the criterion applies to metrics of negative sectional curvature which are in the same conformal class as a metric of constant negative sectional curvature.
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