Identifying ballistic modes via Poincar\'e sections

TL;DR

This paper introduces an image processing method to efficiently identify and classify chaotic and regular regions in dynamical systems using Poincaré sections, enabling faster detection of superdiffusion in area-preserving maps.

Contribution

The paper presents a novel image-based approach for analyzing Poincaré sections to distinguish dynamical regimes and detect superdiffusion more rapidly than traditional methods.

Findings

Successfully characterized transport regimes in the standard map.

Detected superdiffusion faster than mean square displacement methods.

Applied to a two-wave Hamiltonian to study parameter-dependent superdiffusion.

Abstract

Exploring chaotic systems via Poincar\'e 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 distinguish chaotic and regular regions of area-preserving dynamics, and then 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 much faster 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.