Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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OPENNESS OF ANOSOV FAMILIES

  • Received : 2017.05.07
  • Accepted : 2017.10.25
  • Published : 2018.05.01
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Abstract

Anosov families were introduced by A. Fisher and P. Arnoux motivated by generalizing the notion of Anosov diffeomorphism defined on a compact Riemannian manifold. Roughly, an Anosov family is a two-sided sequence of diffeomorphisms (or non-stationary dynamical system) with similar behavior to an Anosov diffeomorphisms. We show that the set consisting of Anosov families is an open subset of the set consisting of two-sided sequences of diffeomorphisms, which is equipped with the strong topology (or Whitney topology).

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References

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