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arXiv · 1308.3081

Chaotic Systems with Absorption

Eduardo G. Altmann·Jefferson S. E. Portela·Tamás Tél
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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 $κ$ in terms of the natural conditionally-invariant measure of the system; (ii) an increased multifractality when compared to the spectrum of dimensions $D_q$ obtained without taking absorption and return times into account; and (iii) a generalization of the Kantz-Grassberger formula that expresses $D_1$ in terms of $κ$, the positive Lyapunov exponent, the average return time, and a new quantity, the reflection rate. Simulations in the cardioid billiard confirm these results.

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BibTeXRIS

Eduardo G. Altmann, Jefferson S. E. Portela, Tamás Tél. 2013-10-24. Chaotic Systems with Absorption. https://doi.org/10.1103/physrevlett.111.144101

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