Strong anomalous diffusion of the phase of a chaotic pendulum

TL;DR

This paper investigates the anomalous phase diffusion in a driven chaotic pendulum, linking fractal phase space properties to transport phenomena, and introduces a stochastic model that replicates the system's behavior.

Contribution

It reveals the strong anomalous diffusion of the pendulum's phase and connects fractal phase space structures to transport anomalies, proposing a new stochastic modeling approach.

Findings

Demonstrates strong anomalous phase diffusion in the chaotic pendulum

Links fractal phase space properties to transport anomalies

Develops a stochastic model mimicking the system's behavior

Abstract

In this letter we consider the phase diffusion of a harmonically driven undamped pendulum and show that it is anomalous in the strong sense. The role played by the fractal properties of the phase space is highlighted, providing an illustration of the link between deterministic chaos and anomalous transport. Finally, we build a stochastic model which reproduces most properties of the original Hamiltonian system by alternating ballistic flights and random diffusion.