Cascades of Period Multiplying in the Planar Hill’s Problem

Abstract

The task of period multiplying cascade detection in some dynamical systems is a rather complicated problem. The presence of bifurcation chain is not a guarantee that this chain will continue ad infinitum. The indirect confirmation of infinite period multiplying cascade presence is self-duplication of the period muliplying “tree” and convergence of its characteristics to certain universal values. The goal of the present work is to study different period multiplying sequences, e.g. period tripling as well as numerical determination and their Feigenbaum and scaling constants.