Identifying ballistic modes via Poincaré sections

Abstract

Exploring chaotic systems via Poincaré sections has proven essential in dynamical systems, yet measuring their characteristics poses challenges to identify the various dynamical regimes considered. In this paper, we propose a new approach that uses image processing to classify the transport regime. We characterize different transport regimes in the standard map with the proposed method based on image reconstruction techniques, identifying the superdiffusion through the identification of ballistic modes, a method that requires less iterations than the usual mean square displacement method. The procedure is also applied to a two-wave, time-dependent Hamiltonian to investigate superdiffusion in function of two parameters.