Onset of Secular Chaos in Planetary Systems: Period Doubling & Strange Attractors

TL;DR

This paper investigates how planetary systems transition to chaos through period doubling and the existence of strange attractors, especially considering dissipative effects, providing insights into early planetary system evolution.

Contribution

It introduces a novel analysis of chaos onset in planetary systems with dissipation, highlighting the role of period doubling and strange attractors in their dynamical evolution.

Findings

Planetary systems approach chaos via period doubling as dissipation decreases.

Chaotic strange attractors can exist in mildly damped planetary systems.

Results shed light on early dynamical evolution of chaotic planetary systems.

Abstract

As a result of resonance overlap, planetary systems can exhibit chaotic motion. Planetary chaos has been studied extensively in the Hamiltonian framework, however, the presence of chaotic motion in systems where dissipative effects are important, has not been thoroughly investigated. Here, we study the onset of stochastic motion in presence of dissipation, in the context of classical perturbation theory, and show that planetary systems approach chaos via a period-doubling route as dissipation is gradually reduced. Furthermore, we demonstrate that chaotic strange attractors can exist in mildly damped systems. The results presented here are of interest for understanding the early dynamical evolution of chaotic planetary systems, as they may have transitioned to chaos from a quasi-periodic state, dominated by dissipative interactions with the birth nebula.