Can Classical Linear Harmonic Oscillator Hold Chaotic (Fractal) Dynamics

TL;DR

This paper demonstrates that a classical linear harmonic oscillator, when periodically restarted, can exhibit chaotic and fractal dynamics similar to the logistic map, challenging traditional views on chaos.

Contribution

It introduces a mechanism where a linear harmonic oscillator can produce chaotic behavior through periodic restarting, linking classical and quantum chaotic dynamics.

Findings

Oscillator dynamics analogous to logistic map

Chaotic (fractal) behavior observed in linear systems

Quantum systems show similar perturbed dynamics

Abstract

In this work a classical linear harmonic oscillator, evolving during a small time interval (so that simple non-linear, second order Taylor approximation of the dynamics is satisfied) and restarting (by a mechanism) in a strictly chosen series of the time moments, is considered. It is shown that given linear oscillator behaves dynamically analogously to discrete logistic equation, which, as an especial case, includes chaotic (fractal) behaviour too. (All this refers too on the analogous quantum systems, e.g. ammonia molecule with simple vibration dynamics of the atoms many times perturbed by measurements in strictly defined time moments.