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Attractors and orbit-flip homoclinic orbits for star flows


Author: C. A. Morales
Journal: Proc. Amer. Math. Soc. 141 (2013), 2783-2791
MSC (2010): Primary 37D20; Secondary 37C10
DOI: https://doi.org/10.1090/S0002-9939-2013-11535-2
Published electronically: April 12, 2013
MathSciNet review: 3056568
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Abstract: We study star flows on closed $ 3$-manifolds and prove that they either have a finite number of attractors or can be $ C^1$ approximated by vector fields with orbit-flip homoclinic orbits.


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Additional Information

C. A. Morales
Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970 Rio de Janeiro, Brazil
Email: morales@impa.br

DOI: https://doi.org/10.1090/S0002-9939-2013-11535-2
Keywords: Star flow, attractor, orbit-flip homoclinic orbit
Received by editor(s): July 28, 2001
Received by editor(s) in revised form: November 3, 2011
Published electronically: April 12, 2013
Additional Notes: The author was partially supported by CNPq, FAPERJ and PRONEX-Brazil.
Communicated by: Bryna Kra
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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