Spectral properties of chaotic processes
نویسندگان
چکیده
We investigate the spectral asymptotic properties of the stationary dynamical system ξt = φ(T (X0)). This process is given by the iterations of a piecewise expanding map T of the interval [0, 1], invariant for an ergodic probability μ. The initial state X0 is distributed over [0, 1] according to μ and φ is a function taking values in R. We establish a strong law of large numbers and a central limit theorem for the integrated periodogram as well as for Fourier transforms associated with (ξt). Several examples of expanding maps T are also provided. AMS subject classifications. Primay 37A50; secondary 60F05, 60F15.
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