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Dynamical systems with a prescribed globally bp-attracting set and applications to conservative dynamics

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  • Given an arbitrary fixed closed subset $ \mathcal{C}\subset\mathbb{R}^n $, we provide an explicit method to construct a dynamical system which admits the regular part of $ \mathcal{C} $ as globally bp-attracting set, i.e. a closed and invariant set which attracts every bounded positive orbit of the dynamical system. As application, we provide an explicit method of leafwise asymptotic bp-stabilization of the regular part of an a-priori given invariant set of a conservative system. The theoretical results are illustrated for the completely integrable case of the Rössler dynamical system.

    Mathematics Subject Classification: Primary: 34C45; Secondary: 37J15; 70H33.

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