Chaotic Explosions

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.

7 pages, 5 figures

References in corpus (6)

• Leaking Chaotic Systems
• Quasi-Scarred Resonances in a Spiral-Shaped Microcavity
• Survival probability time distribution in dielectric cavities
• Chaos-assisted emission from asymmetric resonant cavity microlasers
• Chaotic Systems with Absorption
• Comparison of averages of flows and maps

Cited by in corpus (7)

• Structure of resonance eigenfunctions for chaotic systems with partial escape
• Chaotic resonance modes in dielectric cavities: Product of conditionally invariant measure and universal fluctuations
• Local random vector model for semiclassical fractal structure of chaotic resonance states
• Semiclassical Limit of Resonance States in Chaotic Scattering
• Consequences of a wave-correction extended ray dynamics for integrable and chaotic optical microcavities
• Ray picture and ray-wave correspondence in triangular microlasers
• Left-Right Husimi Representation of Chaotic Resonance States: Invariance and Factorization