Abstract
This paper represents part of a program to understand the behavior of topological entropy for Anosov and geodesic flows. In this paper, we have two goals. First we obtain some regularity results forC 1 perturbations. Second, and more importantly, we obtain explicit formulas for the derivative of topological entropy. These formulas allow us to characterize the critical points of topological entropy on the space of negatively curved metrics.
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Communicated by J.-P. Eckmann
Partially supported by NSF grant DMS-8514630
Chaim Weizmann Research Fellow and NSF postdoctoral Research Fellow
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Katok, A., Knieper, G. & Weiss, H. Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows. Commun.Math. Phys. 138, 19–31 (1991). https://doi.org/10.1007/BF02099667
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DOI: https://doi.org/10.1007/BF02099667