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Axiom A flows with a transverse torus
Author(s):
C.
A.
Morales
Journal:
Trans. Amer. Math. Soc.
355
(2003),
735-745.
MSC (2000):
Primary 37D20;
Secondary 37E99
Posted:
October 1, 2002
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Abstract:
Let  be an Axiom A flow with a transverse torus  exhibiting a unique orbit  that does not intersect  . Suppose that there is no null-homotopic closed curve in  contained in either the stable or unstable set of  . Then we show that  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:
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
Posted:
October 1, 2002
Additional Notes:
The author was partially supported by FAPERJ, CNPq and PRONEX-Brasil
Copyright of article:
Copyright
2002,
American Mathematical Society
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