Sectional-Anosov flows |
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Authors: | C A Morales |
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Institution: | (2) CMUP, Porto, Portugal;(3) IM-UFRJ, Rio de Janeiro, Brazil;(4) IMPA, Rio de Janeiro, Brazil; |
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Abstract: | We define sectional-Anosov flow as a vector field on a manifold, inwardly transverse to the boundary, whose maximal invariant set is sectional-hyperbolic
(Metzger and Morales in Ergodic Theory Dyn Syst 28:1587–1597, 2008). We obtain properties of sectional-Anosov flows without
null-homotopic periodic orbits on compact irreducible 3-manifolds including: incompressibility of transverse torus, non-existence
of genus 0 transverse surfaces nor hyperbolic attractors nor hyperbolic repellers and sufficient conditions for the existence
of singularities non-isolated in the nonwandering set. These generalize some known facts about Anosov flows. |
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Keywords: | |
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