Smooth conjugacy and S-R-B measures for uniformly and non-uniformly hyperbolic systems
Smooth conjugacy and S-R-B measures for uniformly and non-uniformly hyperbolic systems
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均匀和非均匀双曲系统的平滑共轭和 S-R-B 测量
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发表时间：
1992
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影响因子：
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通讯作者：
Systems R De La Llave
中科院分区：
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作者：
Systems R De La Llave
我们给出了低维Anosov系统光滑共轭的一个新的证明，即相应周期轨道上的特征值构成了一个完整的不变量集。我们还证明了，如果两个光滑低维Anosov系统共轭的同胚是绝对连续的，则它与映射一样光滑。我们进一步证明了这些事实在非一致双曲组中的推广，以及在高维上的推广和反例。
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.