A Positive Solution to a Conjecture of A. Katok for Diffeomorphism Case
نویسندگان
چکیده
A. Katok has conjectured that a C map g : Mn → Mn, n ≥ 2, which is Hölder conjugated to an Anosov diffeomorphism is also an Anosov diffeomorphism. Using Pesin stable manifold theorem and Liao spectrum theorem, we show that under the hypothesis of such a conjecture, g is an Axiom A diffeomorphism having no cycles. Particularly, if g is Hölder conjugated to a hyperbolic toral automorphism, then g is Anosov.
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