IMPA

Preprint serie D 86/2011

Lectures on sectional-Anosov flows

S. Bautista , C. Morales

Keywords:
Anosov Flow, Sectional-Anosov Flow, Vector Field

Abstract:
This work focuses on {\em sectional-Anosov flows}, i.e., vector fields exhibiting a dominated splitting on the maximal invariant set formed by a contracting subbundle and a subbundle where the flow's derivative {\em expands the area of parallelograms}. Indeed, we expose several aspects of the theory of sectional-Anosov flows developed by the authors during the first decate of the twenty one century. The exposition is done in a way to put together both Anosov and sectional-Anosov flows in the same context. Aspects of the theory of Anosov flows are then included for the sake of completeness.

MSC 2000:
37D30    Partially hyperbolic systems and dominated splittings
57N10    Topology of general $3$-manifolds


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