RIGOROUS VERIFICATION OF CHAOS IN A MOLECULAR-MODEL

The Thiele-Wilson system, a simple model of a linear, triatomic molecu le, has been studied extensively in the past. The system exhibits comp lex molecular dynamics including dissociation, periodic trajectories, and bifurcations. In addition, it has for a long time been suspected t o be chaotic, but this has never been proved with mathematical rigor. In this paper, we present numerical results that, using interval metho ds, rigorously verify the existence of transversal homoclinic points i n a Poincare map of this system. By a theorem of Smale, the existence of transversal homoclinic points in a map rigorously proves its mixing property, i.e., the chaoticity of the system.