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Multifractality of the Lorenz system
Physical Review E, 1996We use the unstable periodic orbit expansion of the dynamical \ensuremath{\zeta} function to find the multifractal spectra f(\ensuremath{\alpha}) and g(\ensuremath{\Lambda}) for the Lorenz system at (r,\ensuremath{\sigma},b)=(28,10,8/3) and also for an incomplete, generalized Baker's map with the topology of the Lorenz system. \textcopyright{} 1996 The
, Wiklund, , Elgin
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Multifractal analysis of earthquakes
pure and applied geophysics, 1992Multifractal properties of the epicenter and hypocenter distribution and also of the energy distribution of earthquakes are studied for California, Japan, and Greece. The calculated D q −q curves (the generalized dimension) indicate that the earthquake process is multifractal or heterogeneous in the fractal dimension.
Tadashi Hirabayashi +2 more
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Multifractal diffusion in NASDAQ
Journal of Physics A: Mathematical and General, 2001Summary: It is shown that fluctuations of NASDAQ increments exhibit two scaling intervals: one (for relatively short-time increments, up to five months) is quasi-Brownian and another (for relatively long-time increments) is multifractal. For the multifractal diffusion a new type of scaling symmetry has been observed.
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Multifractional Stochastic Fields
2013Fractional Brownian Motion (FBM) is a very classical continuous self-similar Gaussian field with stationary increments. In 1940, some works of Kolmogorov on turbulence led him to introduce this quite natural extension of Brownian Motion, which, in contrast with the latter, has correlated increments. However, the denomination FBM is due to a very famous
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A relative vectorial multifractal formalism
Chaos, Solitons and Fractals, 2022Amal Mahjoub, Najmeddine Attia
exaly