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Echoes in classical dynamical systems

Bruno Eckhardt

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Echoes arise when external manipulations to a system induce a reversal of its time evolution that leads to a more or less perfect recovery of the initial state. We discuss the accuracy with which a cloud of trajectories returns to the initial state in classical dynamical systems that are exposed to additive noise, and small differences in the equations of motion for forward and backward evolution. The cases of integrable and chaotic motion, and small or large noise are studied in some detail and many different dynamical laws are identified. Experimental tests in two-dimensional flows that show chaotic advection are proposed.


PACS

43.55.+p Architectural acoustics

43.28.+h Aeroacoustics and atmospheric sound

47.52.+j Chaos

43.50.+y Noise: its effects and control

MSC

76Q05 Hydro- and aero-acoustics

76F10 Shear flows

37N05 Dynamical systems in classical and celestial mechanics (See mainly 70Fxx, 70Hxx, 70Kxx)

34C28 Complex behavior, chaotic systems (See mainly 37Dxx)

Subjects

Fluid dynamics

Statistical physics and nonlinear systems

Dates

Issue 2 (17 January 2003)

Received 13 May 2002, in final form 1 October 2002

Published 17 December 2002



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