Punctuated Chaos and Indeterminism in Self-gravitating Many-body Systems

TL;DR

This paper introduces a new model of chaos in self-gravitating systems, where exponential divergence occurs in discrete bursts, leading to potential fundamental indeterminism in astrophysical dynamics.

Contribution

It proposes the concept of punctuated chaos, showing how discrete events cause exponential divergence, differing from traditional continuous chaos models in gravitational systems.

Findings

Punctuated chaos results from discrete events causing exponential divergence.

Long-lived systems can amplify microscopic perturbations to astronomical scales.

Systems with punctuated chaos may be fundamentally indeterministic.

Abstract

Dynamical chaos is a fundamental manifestation of gravity in astrophysical, many-body systems. The spectrum of Lyapunov exponents quantifies the associated exponential response to small perturbations. Analytical derivations of these exponents are critical for understanding the stability and predictability of observed systems. This essay presents a new model for chaos in systems with eccentric and crossing orbits. Here, exponential divergence is not a continuous process but rather the cumulative effect of an ever-increasing linear response driven by discrete events at regular intervals, i.e., punctuated chaos. We show that long-lived systems with punctuated chaos can magnify Planck length perturbations to astronomical scales within their lifetime, rendering them fundamentally indeterministic.