Abstract

Abstract

Abstract

Abstract
For uniformly asymptotically affine (uaa) Markov maps on train tracks, we prove the following type of rigidity result: if a topological conjugacy between them is (uaa) at a point in the train track then the conjugacy is (uaa) everywhere. In particular, our methods apply to the case in which the domains of the Markov maps are Canter sets. We also present similar statements for (uaa:) and C-r Markov families. These results generalize the similar ones of Sullivan and de Faria for C-r expanding circle maps with r > 1 and have useful applications to hyperbolic dynamics on surfaces and laminations.

Abstract
We exploit ideas of nonlinear dynamics in a non-deterministic dynamical setting. Our object of study is the observed riverflow time series of the Portuguese Paiva river whose water is used for public supply. The Takens delay embedding of the daily riverflow time series revealed an intermittent dynamical behaviour due to precipitation occurrence. The laminar phase occurs in the absence of rainfall. The nearest neighbour method of prediction revealed good predictability in the laminar regime but we warn that this method is misleading in the presence of rain. The correlation integral curve analysis, Singular Value Decomposition and the Nearest Neighbour Method indicate that the laminar regime of flow is in a small neighbourhood of a one-dimensional affine subspace in the phase space. The Nearest Neighbour method attested also that in the laminar phase and for a data set of 53 years the information of the current runoff is by far the most relevant information to predict future runoff. However the information of the past two runoffs is important to correct non-linear effects of the riverflow as the MSE and MRE criteria results show. The results point out that the Nearest Neighbours method fails when used in the irregular phase because it does not predict precipitation occurrence. © 2007, Birkhäuser Verlag Basel/Switzerland.

Abstract
We consider the. re-scaled PSI20 daily index positive returns r(t)(alpha) and negative returns (-r(t))(alpha) called, after normalization, the. positive and negative fluctuations, respectively. We use the Kolmogorov-Smirnov statistical test as a method to find the values of alpha that optimize the data collapse of the histogram of the. fluctuations with the truncated Bramwell-Holdsworth-Pinton (BHP) probability density function (pdf) fBHP and the truncated generalized log-normal pdf fLN that best approximates the truncated BHP pdf. The optimal parameters we found are alpha(+)(BHP) = 0.48, alpha(-)(BHP) = 0.46, alpha(+)(LN) = 0.50 and alpha(-)(LN) = 0.49. Using the optimal alpha's we compute the analytical approximations of the pdf of the normalized positive and negative PSI20 index daily returns r(t). Since the BHP probability density function appears in several other dissimilar phenomena, our result reveals a universal feature of the stock exchange markets.