# American Institute of Mathematical Sciences

May  2020, 40(5): 3013-3030. doi: 10.3934/dcds.2020159

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

 West University of Timişoara, Faculty of Mathematics and Computer Science, Department of Mathematics, Blvd. Vasile Pȃrvan, No. 4, 300223–Timişoara, Romȃnia

Received  November 2019 Revised  December 2019 Published  March 2020

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.

Citation: Răzvan M. Tudoran. Dynamical systems with a prescribed globally bp-attracting set and applications to conservative dynamics. Discrete & Continuous Dynamical Systems, 2020, 40 (5) : 3013-3030. doi: 10.3934/dcds.2020159
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