Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape ratesL. A. Bunimovich1 and C. P. Dettmann2
1 Applied & Biological Contemporary Mathematics Program, Georgia Institute of Technology Atlanta, GA 30332-1060, USA
2 School of Mathematics, University of Bristol - Bristol BS8 1TW, UK
received 17 July 2007; accepted in final form 14 September 2007; published November 2007
published online 10 October 2007
One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order, the escape rate of chaotic systems is proportional to the hole size and independent of position. Here we give exact formulas for the subsequent terms, as sums of correlation functions; these depend on hole size and position, hence yield information on the closed system dynamics. Conversely, the theory can be readily applied to experimental design, for example to control escape rates.
05.45.-a - Nonlinear dynamics and chaos.
05.60.Cd - Classical transport.
© Europhysics Letters Association 2007