Abstract
The theory of Anosov systems is a result of the generalization of certain properties, which hold on geodesic flows on manifolds of negative curvature. It turned out that these properties alone are sufficient to ensure ergodicity, mixing, and, moreover, existence of K-partitions. All above-mentioned properties are connected with the asymptotical behavior of variational equations along the trajectories of Anosov systems. Therefore, it would be appropriate to propose that other asymptotical properties of geodesic flows on manifolds of negative curvature hold for the class of Anosov systems, too. However, it would be more rational to consider not all of the Anosov flows, but the class L of Anosov flows that preserve some integral invariant and have no continuous eigenfunctions.
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References
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Margulis, G.A. (2004). On Some Aspects of the Theory of Anosov Systems. In: On Some Aspects of the Theory of Anosov Systems. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09070-1_1
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DOI: https://doi.org/10.1007/978-3-662-09070-1_1
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