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          Institute: MPI für Physik Komplexer Systeme     Collection: Deterministic dynamics     Display Documents



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ID: 676369.0, MPI für Physik Komplexer Systeme / Deterministic dynamics
Chaotic Systems with Absorption
Authors:Altmann, E. G.; Portela, J. S. E.; Tel, T.
Date of Publication (YYYY-MM-DD):2013-09-30
Title of Journal:Physical Review Letters
Volume:111
Issue / Number:14
Sequence Number of Article:144101
Review Status:Internal review
Audience:Not Specified
Abstract / Description: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.
External Publication Status:published
Document Type:Article
Communicated by:Vivien Scherr
Affiliations:MPI für Physik Komplexer Systeme
Identifiers:ISI:000325366100005 [ID No:1]
ISSN:0031-9007 [ID No:2]
DOI:10.1103/PhysRevLett.111.144101
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