Related papers: Multifractals via recurrence times ?
The attractors of a dynamical system govern its typical long-term behaviour. The presence of many attractors is significant as it means the behaviour is heavily dependent on the initial conditions. To understand how large numbers of…
Multipole moments carry a lot of information about the gravitational field. Nonetheless, knowing all the multipole moments of an object does not determine conclusively the nature of the object itself. In particular, the multipole moments of…
An efficient method of exploring the effects of anisotropy in the fractal properties of 2D surfaces and images is proposed. It can be viewed as a direction-sensitive generalization of the multifractal detrended fluctuation analysis (MFDFA)…
We discuss a problem initially thought for the Mathematical Olympiad but which has several interpretations. The recurrence sequences involved in this problem may be generalized to recurrence sequences related to a much larger set of…
At low Reynolds numbers, the hydrodynamic interaction between dumbbells driven by an external rotating field can be attractive or repulsive. Dumbbells of dissimilar asymmetric shape or different coupling to the external field undergo…
A frequently encountered situation in the study of delay systems is that the length of the delay time changes with time, which is of relevance in many fields such as optics, mechanical machining, biology or physiology. A characteristic…
In this paper we improve drastically the estimate for the multiplicity of a binary recurrence. The main contribution comes from an effective version of the Faltings' Product Theorem.
Johansson, Jordan, \"Oberg and Pollicott ( Israel J. Math.(2010)) has studied the multifractal analysis of a class of one-dimensional non-uniformly hyperbolic systems, by introducing some new techniques, we extend the results to the case of…
In these lectures I give an introduction to the time-dependent approach to inverse scattering, that has been developed recently. The aim of this approach is to solve various inverse scattering problems with time-dependent methods that…
The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…
Recurrence networks are complex networks, constructed from time series data, having several practical applications. Though their properties when constructed with the threshold value \epsilon chosen at or just above the percolation threshold…
Fractional calculus represents a natural tool for describing relativistic phenomena in pseudo-Euclidean space-time. In this study, Fractional modified special relativity is presented. We obtain fractional generalized relation for the time…
This paper presents analysis of 30 literary texts written in English by different authors. For each text, there were created time series representing length of sentences in words and analyzed its fractal properties using two methods of…
Recurrence plot based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the…
The article discusses building models based on the reconstructed attractors of the time series. Discusses the use of the properties of dynamical chaos, namely to identify the strange attractors structure models. Here is used the group…
The multitime multiple recurrences are common in analysis of algorithms, computational biology, information theory, queueing theory, filters theory, statistical physics etc. The theoretical part about them is little or not known. That is…
We estimate numerically the regularities of a family of Strange Non--Chaotic Attractors related with one of the models studied in C. Grebogy et al. (1984) (see also G. Keller (1996)). To estimate these regularities we use wavelet analysis…
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…
Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts…
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…