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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Peixoto’s conjecture for flows on non-orientable 2-manifolds
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by Carlos Gutierrez and Benito Pires PDF
Proc. Amer. Math. Soc. 133 (2005), 1063-1074 Request permission


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
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  • Benito Pires
  • Affiliation: Departamento de Matemáticas, Universidad Autonoma de Barcelona, Edificio C, Bellaterra, Cerdanyola del Valles, Spain
  • Email:
  • 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
  • © Copyright 2004 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 1063-1074
  • MSC (2000): Primary 34D30, 37E05, 37E35; Secondary 37C20
  • DOI:
  • MathSciNet review: 2117207