Liapunov Spectra for Infinite Chains of Nonlinear Oscillators
نویسنده
چکیده
We argue that the spectrum of Liapunov exponents for long chains of nonlinear oscillators, at large energy per mode, may be well approximated by the Liapunov exponents of products of independent random matrices. If, in addition, statistical mechanics applies to the system, the elements of these random matrices have a distribution which may be calculated from the potential and the energy alone. Under a certain isotropy hypothesis (which is not always satis ed) we argue that the Liapunov exponents of these random matrix products can be obtained from the density of states of a typical random matrix. This construction uses an integral equation rst derived by Newman. We then derive and discuss a method to compute the spectrum of a typical random matrix. Putting the pieces together we see that the Liapunov spectrum can be computed from the potential between the oscillators. 2
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