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Название: A Very Spectral Band
Автор: Lorenz E.N.
The power spectrum of the variable z in the Lorenz equations with o = 10, b = 8/3, and r = 200 appeared in previous work to contain a line superposed on a continuum. Analysis of an extended solution into consecutive segments with rather Similar initial states, each segment spanning at least seven maxima of z, shows that the apparent line is actually a narrow band. Solutions spanning at least 14000 maxima of z wouId be needed to resolve the band by standard computation procedures. Multiplication of the right side of each equation by the same function can convert the band to a line, while leaving the points of the attractor unchanged. It is proposed that the spectrum of a completely coupled autonomous flow is, in a certain sense, unlikely to contain a superposition of lines and a continuum.