Publication at Faculty of Mathematics and Physics |
2015
Abstract
A local geometrical criterion for chaos, based on an embedding of a Hamiltonian system into an appropriately chosen curved space, is applied in the classical version of the Geometric Collective Model of nuclei. The criterion is shown to be equivalent with a simpler indicator of chaos based on the convex-concave change of equipotential curves.
It is tested by comparing its predictions with a detailed numerical analysis of global dynamics. The results indicate a capacity of the method to estimate the energy of the onset of chaos, but also demonstrate convincing counterexamples that disprove its general applicability.