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Robust attractors without dominated splitting on manifolds with boundary

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  • In this paper we prove that there exists a positive integer $k$ with the following property: Every compact $3$-manifold with boundary carries a $C^\infty$ vector field exhibiting a $C^k$-robust attractor without dominated splitting in a robust sense.
    Mathematics Subject Classification: Primary: 34D45, 37D30; Secondary: 37C10, 37F15, 37D99.


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