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

RĂazvan M. Tudoran

doi:10.3934/dcds.2020159

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2020, Volume 40, Issue 5: 3013-3030. Doi: 10.3934/dcds.2020159

This issue Previous Article Local well-posedness for Navier-Stokes equations with a class of ill-prepared initial data Next Article

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

RĂazvan M. Tudoran

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

Received: October 31, 2019

Revised: November 30, 2019

Published: March 2020

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Abstract

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.

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

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