Chaotic Explosions

TL;DR

This paper studies chaotic systems with unbounded trajectory intensities, revealing exponential growth, fractal spatial distributions, and differences from absorbing systems, supported by simulations and analytical models.

Contribution

It introduces an operator formalism for exploding chaotic systems and highlights the differences between explosion and absorption dynamics.

Findings

Intensity grows exponentially over time.

Spatial distribution follows a fractal measure with lower information dimension.

Invariant quantities for explosion differ from those in absorption.

Abstract

We investigate chaotic dynamical systems for which the intensity of trajectories might grow unlimited in time. We show that (i) the intensity grows exponentially in time and is distributed spatially according to a fractal measure with an information dimension smaller than that of the phase space,(ii) such exploding cases can be described by an operator formalism similar to the one applied to chaotic systems with absorption (decaying intensities), but (iii) the invariant quantities characterizing explosion and absorption are typically not directly related to each other, e.g., the decay rate and fractal dimensions of absorbing maps typically differ from the ones computed in the corresponding inverse (exploding) maps. We illustrate our general results through numerical simulation in the cardioid billiard mimicking a lasing optical cavity, and through analytical calculations in the baker map.