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| In the research of Palis conjecture, one is interesting with some Lyapunov stable chain recurrent classes. For the case of vector fields, we would like to study the properties of some singularity which is contained in a Lyapunov stable chain recurrent class. We prove that for a generic vector field which is far away from homoclinic tangencies, if a singularity is contained in a non-trivial Lyapunov stable chain recurrent class, then the singularity has some strong stable manifold, which intersects the chain recurrent class only at the singularity. |
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| Keywords:dynamical system, vector field, chain recurrent class, singularity, strong stable manifold |
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