On the approximation of time one maps of Anosov flows by Axiom A diffeomorphisms

Abstract.

We prove that if 𝒻₁ is the time one map of a transitive and codimension one Anosov flow φ and it is C ¹-approximated by Axiom A diffeomorphisms satisfying a property called P, then the flow is topologically conjugated to the suspension of a codimension one Anosov diffeomorphism. A diffeomorphism 𝒻 satisfies property P if for every periodic point in M the number of periodic points in a fundamental domain of its central manifold is constant.