相关论文: Multifractality of the Feigenbaum attractor and fr…
It is shown phenomenologically that the fractional derivative $\xi=D^\alpha u$ of order $\alpha$ of a multifractal function has a power-law tail $\propto |\xi| ^{-p_\star}$ in its cumulative probability, for a suitable range of $\alpha$'s.…
We use the theory of Bernstein functions to analyze power law tail behavior with log-periodic perturbations which corresponds to self-similarity of the Bernstein functions. Such tail behavior appears in the context of semistable L\'evy…
Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…
We analyze quantitatively the effect of spurious multifractality induced by the presence of fat-tailed symmetric and asymmetric probability distributions of fluctuations in time series. In the presented approach different kinds of symmetric…
Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of multifractality in the time series. Series fluctuating according to a qGaussian…
We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…
Based on the mathematical arguments formulated within the Multifractal Detrended Fluctuation Analysis (MFDFA) approach it is shown that in the uncorrelated time series from the Gaussian basin of attraction the effects resembling…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
Detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency Deutsche Aktienindex data. The tail index ($\alpha$), the Renyi exponents…
In this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process. We also study the heavy (power-law) tail behavior of probability density function associated with…
We study multifractal properties in time evolution of a single particle subject to repeated measurements. For quantum systems, we consider circuit models consisting of local unitary gates and local projective measurements. For classical…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
We demonstrate that the harmonic inversion technique is a powerful tool to analyze the spectral properties of optical microcavities. As an interesting example we study the statistical properties of complex frequencies of the fully chaotic…
We derive the multifractal analysis of the conformal measure (or equivalently, the invariant measure) associated to a family of weights imposed upon a (multi-dimensional) graph directed Markov system (GDMS) using balls as the filtration.…
Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. Most of the previous studies concentrated on fine-tuned quantum models to realize multifractality which is generally…
Classical, self-consistent theory of statistical mechanics was developed for the thermodynamic and conservative Hamiltonian systems. Later there were many attempts (Sinai-Bowen-Ruelle's temperature, Tsallis' non-extensive theory) to apply…
Multifractals are inhomogeneous measures (or functions) which are typically described by a full spectrum of real dimensions, as opposed to a single real dimension. Results from the study of fractal strings in the analysis of their geometry,…
Macroscopic systems often display phase transitions where certain physical quantities are singular or self-similar at different (spatial) scales. Such properties of systems are currently characterized by some order parameters and a few…
The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves…