INTERMITTENCY, PHASE RANDOMIZATION AND GENERALIZED FRACTAL DIMENSIONS
The procedure of Fourier phase randomization has been repeatedly proposed for distinguishing low-dimensional chaos from noise in a measured time series. Here we extend the use of this method and we show that phase randomization is a necessary step for assessing the presence of intermittency in a stochastic and/or turbulent system. This procedure allows us to distinguish between linear and nonlinear signals as well. As an example of application of this approach, we study the time series of positions of passively advected particles in 2D turbulence and we show that their apparent multifractality is not associated with intermittency. The results discussed here confirm the importance of understanding the phase spectrum, and of developing appropriate measures of the phase distribution, in the study of nonlinear systems.
Let W be a UHF algebra and sQ(D) the disk algebra. If W = [U,ll >1 I ]Jand a is a product-type automorphism of W which leaves each 21,, invariant, then a defines an embedding t1 2>(D) n+ 1 D The inductive limit of this system is a Banach algebra whose maximal ideal space is closely related to that of the disk algebra if the Connes spectrum F(a) is finite.