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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



$ {\rm SO}(2)$-equivariant vector fields on $ 3$-manifolds: moduli of stability and genericity

Authors: Genesio Lima dos Reis and Geovan Tavares dos Santos
Journal: Trans. Amer. Math. Soc. 308 (1988), 747-763
MSC: Primary 58F10; Secondary 58F09
MathSciNet review: 951626
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Abstract: An open and dense class of vector fields on $ 3$-dimensional compact manifolds equivariant under the action of $ \operatorname{SO} (2)$ is defined. Each such vector field has finite moduli of stability. We also exhibit an open and dense subset of the $ \operatorname{SO} (2)$-equivariant gradient vector fields which are structurally stable.

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Keywords: Compact Lie group, equivariant vector field, normal hyperbolicity, stratumwise transversality, moduli of stability
Article copyright: © Copyright 1988 American Mathematical Society