Chaotic Systems with Absorption

Altmann, E. G.; Portela, J. S. E.; Tel, T.

doi:10.1103/PhysRevLett.111.144101

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Chaotic Systems with Absorption

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Altmann, E. G.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Portela, J. S. E.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Altmann, E. G., Portela, J. S. E., & Tel, T. (2013). Chaotic Systems with Absorption. Physical Review Letters, 111(14): 144101. doi:10.1103/PhysRevLett.111.144101.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-8576-5

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 kappa 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 kappa, the positive Lyapunov exponent, the average return time, and a new quantity, the reflection rate. Simulations in the cardioid billiard confirm these results.