Maximal transitive sets with singularities for genericC 1 vector fields
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A transitive set Λ of a vector fieldX ismaximal transitive if it contains every transitive set ofX intersecting it. We shall prove that ifX isC 1 generic then every singularity ofX with either only one positive or only one negative eigenvalue belongs to a maximal transitive set ofX. In particular, we characterize maximal transitive sets with singularities for genericC 1 vector fields on closed 3-manifolds in terms of homoclinic classes associated to a unique singularity. We apply our results to the examples introduced in  and .
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- Maximal transitive sets with singularities for genericC 1 vector fields
Boletim da Sociedade Brasileira de Matemática - Bulletin/Brazilian Mathematical Society
Volume 31, Issue 3 , pp 287-303
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- transitive sets
- maximal transitive sets
- transitive sets with singularities