Economists have widely applied the correlation integral of Grassberger and Procaccia (1983) to determine the dimension of a nonlinear dynamical system. A key judgmental input into this procedure is the choice of delay time for reconstructing a possible attractor. The literature, however, lacks a rigorous procedure for choosing the delay time. In this paper, I apply a simple nonparametric test f...

Standard cosmology is based on the assumption that the universe is spatially homogeneous. However the consensus on a homogeneous matter structure, even on very large scales, has never been complete. The advantage of correlation dimension calculations is that they enable one to obtain the transition scale to a homogeneous distribution, whereas other methods, such as those using the two-point cor...

In the 1980s, there were numerous claims, based on estimates of the correlation dimension, that the variability of various geophysical processes, in particular rainfall, is generated by a low-dimensional deterministic chaos. Due to a recent attempt (Sivakumar et ai, 2001) to revive the same approach and with claims of an analogous result for the rainfall-runoff process, we think it is necessary...

We consider self-similar Cantor sets Λ ⊂ R which are either homogeneous and Λ− Λ is an interval, or not homogeneous but having thickness greater than one. We have a natural labeling of the points of Λ which comes from its construction. In case of overlaps among the cylinders of Λ, there are some “bad” pairs (τ, ω) of labels such that τ and ω label the same point of Λ. We express how much the co...

chaos theory discusses unstable and non-periodic behavior of non-linear fluctuating dynamicsystems. since evaporation level variations of lakes have a dynamic identity, chaos theory can have a uniquerole in collecting data of these variations. therefore it is an important and challenging problem in the field ofplanning and qualitative and quantitative management of urmia lake to verify whether ...

Abstract. We study the one-dimensional potential-scattering problem when the potential is a Radon measure with compact support. We show that the usual reflection and transmission amplitude r(p) and t (p) of an incoming wave eipx are well defined. We also show that the scattering problem on fractal potentials can be obtained as a limit case of scattering on smooth potentials. We then explain how...

We investigate the behaviour of galaxy clustering on large scales using the PSCz catalogue. In particular, we ask whether there is any evidence of large-scale fractal behaviour in this catalogue. We find the correlation dimension in this survey varies with scale, consistent with other analyses. For example, our results on small and intermediate scales are consistent those obtained from the QDOT...

Present paper deals with mean monthly total ozone concentration over Arosa, Switzerland. The basic rationale is to investigate the existence of chaos within the relevant time series. Method of correlation dimension is adopted here as the research methodology. After a rigorous investigation a low dimensional chaos is identified within the time series pertaining to mean monthly total ozone concen...

The purpose of this study is to build a relaxation system which can control a user’s body condition, changing the operation mode and intensity of the massage seat according to the user current condition. Heart rate is an index of human conditions which can be easily measured, and it has chaotic dynamics. In this paper, we show relations between the intensity of the massage operation and two ind...