Fang, Yong Thermodynamic invariants of Anosov flows and rigidity. (English) Zbl 1167.37305 Discrete Contin. Dyn. Syst. 24, No. 4, 1185-1204 (2009). Summary: By using a formula relating topological entropy Encyclopedia of Mathematics Wikipedia Wolfram MathWorld and cohomological pressure, we obtain several rigidity results about contact Anosov flows Wikipedia Wolfram MathWorld Wolfram MathWorld . For example, we prove the following result: Let \(\varphi \) be a \(C^\infty \) contact Anosov flow. If its Anosov splitting is \(C^2\) and it is \(C^0\) orbit equivalent to the geodesic flow Encyclopedia of Mathematics nLab nLab Wikipedia Wolfram MathWorld of a closed negatively curved Riemannian manifold, then the cohomological pressure and the metric entropy Encyclopedia of Mathematics Wikipedia Wolfram MathWorld of \(\varphi \) coincide. This result generalizes a result of U. Hamenstädt [Math. Ann. 301, No. 4, 677–698 (1995; Zbl 0821.58033)] for geodesic flows. Cited in 7 Documents MSC: 37A35 Entropy and other invariants, isomorphism, classification in ergodic theory 34D20 Stability of solutions to ordinary differential equations 37D35 Thermodynamic formalism, variational principles, equilibrium states for dynamical systems 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) Keywords:anosov flow; entropy; cohomological pressure Citations:Zbl 0821.58033 × Cite Format Result Cite Review PDF Full Text: DOI