DYNAMICAL SYSTEMS WITH A PRESCRIBED GLOBALLY BP-ATTRACTING SET AND APPLICATIONS TO CONSERVATIVE DYNAMICS

摘要

Given an arbitrary fixed closed subset C ⊂ R~n, we provide an explicit method to construct a dynamical system which admits the regular part of 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 Rossler dynamical system.