Abstract
We prove that all nonwandering points of a sectional-Anosov flow on a compact 3-manifold can be approximated by periodic points or by points for which the omega-limit set is a singularity. This improves the closing lemma in Morales (Mich. Math. J. 56(1):29–53, 2008). We also describe a sectional-Anosov flow for which the recurrent points are not dense in the nonwandering set.
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This work was partially supported by CNPq, FAPERJ and PRONEX/DYN-SYS from Brazil.
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Morales, C.A. An improved sectional-Anosov closing lemma. Math. Z. 268, 317–327 (2011). https://doi.org/10.1007/s00209-010-0673-x
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DOI: https://doi.org/10.1007/s00209-010-0673-x