相关论文: Multifractals via recurrence times ?
We consider the existence of robust strange nonchaotic attractors (SNA's) in a simple class of quasiperiodically forced systems. Rigorous results are presented demonstrating that the resulting attractors are strange in the sense that their…
We achieve the multifractal analysis of a class of complex valued statistically self-similar continuous functions. For we use multifractal formalisms associated with pointwise oscillation exponents of all orders. Our study exhibits new…
In this paper, we revisit one-channel time reversal (TR) experiments through multiple scattering media in the framework of the self-consistent multiple scattering theory. The hyper resolution and the self-averaging property are retrieved.…
Recurrence plots and recurrence quantification analysis have become popular in the last two decades. Recurrence based methods have on the one hand a deep foundation in the theory of dynamical systems and are on the other hand powerful tools…
The creativity and emergence of biological and psychological behavior are nonlinear. However, that does not necessarily mean only that the measurements of the behaviors are curvilinear. Furthermore, the linear model might fail to reduce…
The method of reconstruction of an attractor from a set of short time series ({\it clusters}) is proposed and discussed. This method is most useful for correlation dimension estimation of experimental data.
We make some comments about the results we obtained in Phys. Rev. Lett. 86,3392(2001), and in Phys. Rev. Lett.87, 177206 (2001), and show that the conclusion of a recent paper [cond-mat/0409495] leveling some criticism on our results is, in…
Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the…
Reflected random walk in higher dimension arises from an ordinary random walk (sum of i.i.d. random variables): whenever one of the reflecting coordinates becomes negative, its sign is changed, and the process continues from that modified…
In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…
The inverse acoustic scattering of point objects using multi-frequency sparse measurements are studied. The objects may be a sum of point sources or point like scatterers. We show that the locations and scattering strengths of the point…
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…
Logical theories have been developed which have allowed temporal reasoning about eventualities (a la Galton) such as states, processes, actions, events, processes and complex eventualities such as sequences and recurrences of other…
Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system's behaviour in phase space. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late…
We discuss the origin of multiscaling in financial time-series and investigate how to best quantify it. Our methodology consists in separating the different sources of measured multifractality by analysing the multi/uni-scaling behaviour of…
In this brief semi-expository article we present a few efficient techniques for calculating and proving determinantal identities. Several stimulating examples of different flavor and applications are spread across the pages which we hope…
In this paper, we analyze several instrumental records of temperatures at different locations by using new techniques originally developed for the analysis of extreme values of dynamical systems. We show that they have the same recurrence…
This is a short review in honor of B. Mandelbrot's 80st birthday, to appear in W ilmott magazine. We discuss how multiplicative cascades and related multifractal ideas might be relevant to model the main statistical features of financial…
We reveal a general explicit relation between the statistics of delay times in one-channel reflection from a mesoscopic sample of any spatial dimension and the statistics of the eigenfunction intensities in its closed counterpart. This…
In this paper we investigate how many periodic attractors maps in a small neighbourhood of a given map can have. For this purpose we develop new tools which help to make uniform cross-ratio distortion estimates in a neighbourhood of a map…