Asymptotic Stability of Dissipated Hamilton-Poisson Systems

Abstract

We will further develop the study of the dissipation for a Hamilton-Poisson system introduced in 2. We will give a tensorial form of this dissipation and show that it preserves the Hamiltonian function but not the Poisson geometry of the initial Hamilton-Poisson system. We will give precise results about asymptotic stabilizability of the stable equilibria of the initial Hamilton-Poisson system.