Application of the Characteristic Bisection Method for locating and computing periodic orbits in molecular systems

The Characteristic Bisection Method for finding the roots of non-linear algebraic and/or transcendental equations is applied to LiNC/LiCN molecular system to locate periodic orbits and to construct the continuation/bifurcation diagram of the bend mode family. The algorithm is based on the Characteristic Polyhedra which define a domain in phase space where the topological degree is not zero. The results are compared with previous calculations obtained by the Newton Multiple Shooting algorithm. The Characteristic Bisection Method not only reproduces the old results, but also, locates new symmetric and asymmetric families of periodic orbits of high multiplicity.