Chaotic systems with absorption

Eduardo G. Altmann, Jefferson S.E. Portela, Tamás Tél

Research output: Contribution to journalArticle

11 Citations (Scopus)

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

Original languageEnglish
Article number144101
JournalPhysical review letters
Volume111
Issue number14
DOIs
Publication statusPublished - Sep 30 2013

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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