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On Cr-closing for flows on 2-manifolds

Carlos Gutierrez

math.DSarXiv:math/9911188

Abstract

For some full measure subset B of the set of iet's (i.e. interval exchange transformations) the following is satisfied: Let X be a Cr, 1 r ∞, vector field, with finitely many singularities, on a compact orientable surface M. Given a nontrivial recurrent point p∈ M of X, the holonomy map around p is semi-conjugate to an iet E :[0,1) [0,1). If E∈ B then there exists a Cr vector field Y, arbitrarily close to X, in the Cr-topology, such that Y has a closed trajectory passing through p.

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