Chaotic explosions

¹ Max Planck Institute for the Physics of Complex Systems - 01187 Dresden, Germany
² Federal Technological University of Paraná - Pato Branco, PR, Brazil
³ Institute for Theoretical Physics - MTA-ELTE Theoretical Physics Research Group, Eötvös University Budapest, H-1117, Hungary

Received: 19 November 2014
Accepted: 22 January 2015

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.