I. Hosokawa, THEORY OF SCALE-SIMILAR INTERMITTENT MEASURES, Proceedings - Royal Society. Mathematical, physical and engineering sciences, 453(1959), 1997, pp. 691-710
Citations number
42
Journal title
Proceedings - Royal Society. Mathematical, physical and engineering sciences
It is shown that the concept of scale-similar intermittent measures in
troduced by Novikov can be, not only the same as that of the stochasti
c multifractal measures argued by Mandelbrot in the context of negativ
e fractal dimensions, but also the same as that of the vast class of g
eneral stochastic multifractal measures recently introduced by Hentsch
el-but only if a substantial condition is added to the process of ense
mble averaging. The intrinsic probability characterizing the distribut
ion of such a measure is formulated in a general manner so as to be un
iquely related to the so-called singularity spectrum f(alpha), the int
ermittency exponents mu(q) and the generalized dimensions D(q). The tr
ansformation rule of multifractals. the spatial correlations with any
power of such a measure and the special utility of generalized Cantor
sets as multifractals are demonstrated. Finally, the multifractal natu
re of dissipation measure in isotropic turbulence in the inertial rang
e, in which scale-similarity is expected, is discussed in terms of the
se generalized Canter sets.