The paper proves rigidity theorems: if the strong foliation of a perturbation f is mapped to the linear one by the conjugacy h to the toral automorphism L, then h is smooth along the weak foliation and the joint strong-unstable foliation is regular; symmetric results hold for the weak foliation, and
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Cocycles with conjugate periodic data over hyperbolic systems are Holder cohomologous under listed conditions, and topological conjugacies are smooth when derivative cocycles match, implying periodic data rigidity for weakly irreducible hyperbolic automorphisms.
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Rigidity of strong and weak foliations
The paper proves rigidity theorems: if the strong foliation of a perturbation f is mapped to the linear one by the conjugacy h to the toral automorphism L, then h is smooth along the weak foliation and the joint strong-unstable foliation is regular; symmetric results hold for the weak foliation, and
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Periodic data rigidity for cocycles and hyperbolic automorphisms
Cocycles with conjugate periodic data over hyperbolic systems are Holder cohomologous under listed conditions, and topological conjugacies are smooth when derivative cocycles match, implying periodic data rigidity for weakly irreducible hyperbolic automorphisms.