Relaxation rates in chaotic and quasiperiodic systems
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abstract
Relaxation times of arbitrary initial distributions in conservative systems are considered in both quasiperiodic and chaotic systems as modeled by simple two-dimensional maps. Two meaningful characteristic times are introduced: τF, a Fourier space estimate of the longest relaxation time, and τP, a phase space estimate of the time of certain passage. These times, analytically given in terms of the properties of the initial distribution and the system Lyapunov exponents, are shown to be in good agreement with computational results. Extensions to multidimensional systems, cross correlation functions, and continuous time systems are described.
