T. Rage et al., RIGOROUS VERIFICATION OF CHAOS IN A MOLECULAR-MODEL, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 50(4), 1994, pp. 2682-2688
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.