Chaotic systems with absorption

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 Dq obtained without taking absorption and return times into account, and (iii) a generalization of the Kantz-Grassberger formula that expresses D1 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.