  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.
