Successional stability of vector fields in dimension three

A topological invariant, the community transition graph, is introduced for dissipative vector fields that preserve the skeleton of the positive orthan t. A vector field is defined to be successionally stable if it lies in an o pen set of vector fields with the same community transition graph. In dimen sion three, it is shown that vector fields for which the origin is a connec ted component of the chain recurrent set can be approximated in the C-1 Whi tney topology by a successionally stable vector field.