The attractor in usual box-counting methods is partitioned with a fixed grid. We describe an algorithm whose boxes can move into the phase space and adapt to the geometry of the attractor. Lyapunov exponents and the singularity spectrum from time series are estimated using this algorithm.

Multifractional generalizations are considered for kinetic description of chaotic dynamics. The multiplicity of dimensions is motivated by the multiplicity of sticky island hierarchies in phase space. The set of such islands is considered as a singular support that, in the large time...

The complex dynamics between carbon and crude oil markets have been an increasingly interesting area of research. In this paper, we try to take a fresh look at the cross-correlations between carbon and crude oil markets as well as their dynamic behavior employing multifractal detrended...

In this article, we investigated the multifractality and its underlying formation mechanisms in international crude oil markets, namely, Brent and WTI, which are the most important oil pricing benchmarks globally. We attempt to find the answers to the following questions: (1) Are those different...

In this paper, we study the auto-correlations and cross-correlations of West Texas Intermediate (WTI) crude oil spot and futures return series employing detrended fluctuation analysis (DFA) and detrended cross-correlation analysis (DCCA). Scaling analysis shows that, for time scales smaller than...

As one of the fundamental energy sources and important chemical raw materials, crude oil is crucially important to every country. Especially, the price shock of crude oil will bring about hidden dangers in energy security and economic security. Therefore, investigating the dynamics of frequent...

It has been recently noticed that time series of returns in stock markets are of multifractal (multiscaling) character. In that context, multifractality has been always evidenced by its statistical signature (i.e., the scaling exponents associated to a related variable). However, a direct...

Random populations represented by stochastically scattered collections of real-valued points are abundant across many fields of science. Fractality, in the context of random populations, is conventionally associated with a Paretian distribution of the population's values.