Abstract
We give a new proof of the fact that the eigenvalues at corresponding periodic orbits forms a complete set of invariants for the smooth conjugacy of low dimensional Anosov systems. We also show that, if a homeomorphism conjugating two smooth low dimensional Anosov systems is absolutely continuous, then it is as smooth as the maps. We furthermore prove generalizations of these facts for non-uniformly hyperbolic systems as well as extensions and counterexamples in higher dimensions.
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Communicated by J.-P. Eckmann
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de la Llave, R. Smooth conjugacy and S-R-B measures for uniformly and non-uniformly hyperbolic systems. Commun.Math. Phys. 150, 289–320 (1992). https://doi.org/10.1007/BF02096662
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DOI: https://doi.org/10.1007/BF02096662