On Peixoto’s conjecture for flows on non-orientable 2-manifolds
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- by Carlos Gutierrez and Benito Pires PDF
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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 $X.$References
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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
- 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: https://doi.org/10.1090/S0002-9939-04-07687-7
- MathSciNet review: 2117207