Related papers: Multifractal properties of return time statistics
The paper deals with the mathematical - numerical analysis of the Mandelbrot equation extended by the dynamic continuous term. The possibilities of generation of fractal patterns with the mathematical form, defined in such a manner, were…
We suggest an extension of the standard concept of statistical ensembles. Namely, we introduce a class of ensembles with extensive quantities fluctuating according to an externally given distribution. As an example the influence of energy…
We undertake a general study of multifractal phenomena for functions. We show that the existence of several kinds of multifractal functions can be easily deduced from an abstract statement, leading to new results. This general approach does…
The scope of the paper is a theoretical analysis of the dynamical system, the model of which was reduced to Weierstrasse function. A fractal structure of the trajectory was proved and the entropy of the system information designated.
Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within…
We introduce a local multifractal formalism adapted to functions, measures or distributions which display multifractal characteristics that can change with time, or location. We develop this formalism in a general framework and we work out…
The multifractal detrended fluctuation analysis of time series is able to reveal the presence of long-range correlations and, at the same time, to characterize the self-similarity of the series. The rich information derivable from the…
We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…
Erraticity analysis of multiparticle production data is introduced as a way of extracting the maximum amount of information on self-similar fluctuations. It is presented as the next logical step to take beyond the intermittency analysis. An…
Multifractal analysis studies signals, functions, images or fields via the fluctuations of their local regularity along time or space, which capture crucial features of their temporal/spatial dynamics. It has become a standard signal and…
In the statistical description of dynamical systems, an indication of the irreversibility of a given state change is given geometrically by means of a (pre-)ordering of state pairs. Reversible state changes of classical and quantum systems…
We describe in this survey several results relating Fractal Geometry, Dynamical Systems and Diophantine Approximations, including a description of recent results related to geometrical properties of the classical Markov and Lagrange spectra…
The paper presents a unified approach to different fluctuation relations for classical nonequilibrium dynamics described by diffusion processes. Such relations compare the statistics of fluctuations of the entropy production or work in the…
The role played by non extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics has been discussed in details in many works and…
We prove that for conformal expanding maps the return time does have constant multifractal spectrum. This is the counterpart of the result by Feng and Wu in the symbolic setting.
Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
We introduce a framework to identify Fluctuation Relations for vector-valued observables in physical systems evolving through a stochastic dynamics. These relations arise from the particular structure of a suitable entropic functional and…
We study the problem of irreversibility when the dynamical evolution of a many-body system is described by a stochastic quantum circuit. Such evolution is more general than a Hamiltonian one, and since energy levels are not well defined,…
We compare the statistical fluctuation properties of the baryon and meson experimental mass spectra with those obtained from theoretical models (quark models and lattice QCD). We find that for the experimental spectra the statistical…