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

 

Structural stability for flows on the torus with a cross-cap


Author: Carlos Gutiérrez
Journal: Trans. Amer. Math. Soc. 241 (1978), 311-320
MSC: Primary 58F10; Secondary 34C05, 57R25, 58F09
MathSciNet review: 492303
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Abstract: Let $ {{\mathcal{X}}^r}({\tilde M}), r \geq 1$, denote the space of $ {C^r}$-vector fields on the torus with a cross-cap $ \tilde M$. We show that the Morse-Smale vector fields of $ {{\mathcal{X}}^r}({\tilde M})$ are dense on it. We also give a simple proof that a $ {C^0}$-flow on the Klein bottle cannot support a nontrivial $ \omega $-recurrent trajectory.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0492303-2
PII: S 0002-9947(1978)0492303-2
Keywords: Structurally stable, Morse-Smale vector field, nontrivial $ \omega $-recurrent trajectory, transverse circle to flows
Article copyright: © Copyright 1978 American Mathematical Society



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