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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Axiom A flows with a transverse torus


Author: C. A. Morales
Journal: Trans. Amer. Math. Soc. 355 (2003), 735-745
MSC (2000): Primary 37D20; Secondary 37E99
Published electronically: October 1, 2002
MathSciNet review: 1932723
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Abstract: Let $X$ be an Axiom A flow with a transverse torus $T$ exhibiting a unique orbit $O$ that does not intersect $T$. Suppose that there is no null-homotopic closed curve in $T$ contained in either the stable or unstable set of $O$. Then we show that $X$ has either an attracting periodic orbit or a repelling periodic orbit or is transitive. In particular, an Anosov flow with a transverse torus is transitive if it has a unique periodic orbit that does not intersect the torus.


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Additional Information

C. A. Morales
Affiliation: Instituto de Matematica, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, Brazil
Email: morales@impa.br

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03127-6
PII: S 0002-9947(02)03127-6
Keywords: Anosov flow, Axiom A flow, transverse torus
Received by editor(s): October 8, 2001
Received by editor(s) in revised form: February 7, 2002
Published electronically: October 1, 2002
Additional Notes: The author was partially supported by FAPERJ, CNPq and PRONEX-Brasil
Article copyright: © Copyright 2002 American Mathematical Society