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| A smooth vector field will generate a smooth flow. The linearization of the flow with respect to the space variable is called the tangent flow. For an invariant set, one can define the hyperbolic splitting, the partially hyperbolic splitting and the dominated splitting of the tangent flow. We will prove that under some condition, i.e., the set is a weekly transitive set, and the set contains only hyperbolic singularities, then the dominated splitting of the tangent flow on the set implies the partially hyperbolic splitting. |
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| Keywords:dynamical system, vector field, tangent flow, dominated splitting, partially hyperbolic |
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