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

 

On Peixoto's conjecture for flows on non-orientable 2-manifolds


Authors: Carlos Gutierrez and Benito Pires
Journal: Proc. Amer. Math. Soc. 133 (2005), 1063-1074
MSC (2000): Primary 34D30, 37E05, 37E35; Secondary 37C20
Published electronically: November 3, 2004
MathSciNet review: 2117207
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Abstract: Contrary to the case of vector fields on orientable compact $2$-manifolds, there is a smooth vector field $X$ on a non-orientable compact $2$-manifold with a dense orbit (and therefore without closed orbits) whose phase portrait -up to topological equivalence- remains intact under a one-parameter family of twist perturbations localized in a flow box of $X.$


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Additional Information

Carlos Gutierrez
Affiliation: Departamento de Matemática, Institituo de Ciências Matemáticas e de Computaçâo, Universidade de São Paulo, Av. do Trabalhador São Carlense, 400, Centro, CEP 13560-970 São Carlos - SP, Brazil
Email: gutp@icmc.usp.br

Benito Pires
Affiliation: Departamento de Matemáticas, Universidad Autonoma de Barcelona, Edificio C, Bellaterra, Cerdanyola del Valles, Spain
Email: bpires@icmc.usp.br

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07687-7
PII: S 0002-9939(04)07687-7
Received by editor(s): November 2, 2003
Published electronically: November 3, 2004
Additional Notes: The first author was supported in part by Pronex/CNPq/MCT grant number 66.2249/1997-6
The second author was supported by Fapesp grant number 01/04598-0
Communicated by: Michael Handel
Article copyright: © Copyright 2004 American Mathematical Society