Rigorous verification of chaos in a molecular model

Abstract

The Thiele-Wilson system, a simple model of a linear, triatomic molecule, has been studied extensively in the past. The system exhibits complex molecular dynamics including dissociation, periodic trajectories, and bifurcations. In addition, it has for a long time been suspected to be chaotic, but this has never been proved with mathematical rigor. In this paper, we present numerical results that, using interval methods, rigorously verify the existence of transversal homoclinic points in a Poincaré 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. DOI: http://dx.doi.org/10.1103/PhysRevE.50.2682 © 1994 The American Physical Society