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Asymptotic Maslov indices

Abstract : We study the asymptotic Maslov index for surface diffeomorphisms. Roughly speaking,this quantity is the limit of the average rotational velocity of tangent vectors which evolveunder the action of the differential of the diffeomorphism. For twist maps on the annulus,we prove that the set of points of zero index has Hausdorff dimension at least one. In theframework of conservative twist maps, we show that every bounded instability region has apositive Lebesgue measure set of points with non zero index. Finally, we study such indexin the presence of periodic hyperbolic points with transverse homoclinic intersections,providing examples of points at which the asymptotic Maslov index does not exist.
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Anna Florio. Asymptotic Maslov indices. Symplectic Geometry [math.SG]. Université d'Avignon, 2019. English. ⟨NNT : 2019AVIG0422⟩. ⟨tel-02363202v2⟩

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