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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A dichotomy for higher-dimensional flows


Authors: A. Arbieto and C. A. Morales
Journal: Proc. Amer. Math. Soc. 141 (2013), 2817-2827
MSC (2010): Primary 37D30; Secondary 37C10
Published electronically: April 17, 2013
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Abstract: We analyze the dichotomy between sectional-Axiom A flows and flows with points accumulated by periodic orbits of different indices. Indeed, this is proved for $ C^1$ generic flows whose singularities accumulated by periodic orbits have codimension one. Our result improves the work of M. J. Pacifico and the second author.


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Additional Information

A. Arbieto
Affiliation: Instituto de Matématica, Universidade Federal do Rio de Janiero, P. O. Box 68530, 21945-970 Rio de Janeiro, Brazil
Email: arbieto@im.ufrj.br

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

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11536-4
PII: S 0002-9939(2013)11536-4
Keywords: Sectional-Axiom A, Morse index, vector field
Received by editor(s): August 8, 2011
Received by editor(s) in revised form: November 7, 2011
Published electronically: April 17, 2013
Additional Notes: This work was partially supported by CNPq, CAPES-Prodoc, FAPERJ and PRONEX/DS from Brazil
Communicated by: Yingfei Yi
Article copyright: © Copyright 2013 American Mathematical Society