Stability of Dynamical Systems

In this paper we present for all who are interested in beam stabilities some recent results obtained in the theoretical studies of the kind problems. The general results concerning the dynamical systems show that between the stable state and chaotic behaviour there is a zone of transition where a beam present an oscillating stability. The main goal of our work is the implementation for the concrete physical systems of some abstract mathematical notions, like attractors and bifurcation, used in the studies on the stability of a general dynamical system.