Chaotic systems in complex phase space

TL;DR

This paper numerically investigates the complex classical trajectories of the kicked rotor and double pendulum, revealing their chaotic transition and similar behaviors in complex phase space over different timescales.

Contribution

It introduces a detailed numerical analysis of chaos in complex phase space for two PT-symmetric models, highlighting their qualitative similarities.

Findings

Both systems exhibit a transition to chaos in complex phase space.

Short-time and long-time behaviors show strong qualitative similarities.

Complex trajectories reveal insights into PT-symmetric dynamical models.

Abstract

This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviors of these two PT-symmetric dynamical models in complex phase space exhibit strong qualitative similarities.