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arxiv: 1911.00618 · v3 · pith:JE6EQ6GMnew · submitted 2019-11-02 · 🧮 math.DS · math.DG

Singular hyperbolicity of C¹ generic three dimensional vector fields

classification 🧮 math.DS math.DG
keywords dimensionalgenericsingularthreevectoranswerciteclosed
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In the paper, we show that for a generic $C^1$ vector field $X$ on a closed three dimensional manifold $M$, any isolated transitive set of $X$ is singular hyperbolic. It is a partial answer of the conjecture in \cite{MP}.

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