Chaotic Systems with Absorption
Chaotic Dynamics
2013-10-25 v2 Classical Physics
Optics
Abstract
Motivated by applications in optics and acoustics we develop a dynamical-system approach to describe absorption in chaotic systems. We introduce an operator formalism from which we obtain (i) a general formula for the escape rate in terms of the natural conditionally-invariant measure of the system; (ii) an increased multifractality when compared to the spectrum of dimensions obtained without taking absorption and return times into account; and (iii) a generalization of the Kantz-Grassberger formula that expresses in terms of , the positive Lyapunov exponent, the average return time, and a new quantity, the reflection rate. Simulations in the cardioid billiard confirm these results.
Cite
@article{arxiv.1308.3081,
title = {Chaotic Systems with Absorption},
author = {Eduardo G. Altmann and Jefferson S. E. Portela and Tamás Tél},
journal= {arXiv preprint arXiv:1308.3081},
year = {2013}
}