Affiliation:
1. Department of Mathematics , Mokwon University , Daejeon , 302-729 , Korea
Abstract
Abstract
We show that if a vector field X has the C
1 robustly barycenter property then it does not have singularities and it is Axiom A without cycles. Moreover, if a generic C
1-vector field has the barycenter property then it does not have singularities and it is Axiom A without cycles. Moreover, we apply the results to the divergence free vector fields. It is an extension of the results of the barycenter property for generic diffeomorphisms and volume preserving diffeomorphisms [1].
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