Physica A 287 (2000) 91–99 www.elsevier.com/locate/physa Low-dimensional dynamics in observables from complex and higher-dimensional systems Murilo S. Baptista a ; ∗ , Iberˆ e L. Caldas a , Mauricio S. Baptista b , Cassio S. Baptista c , Andr e A. Ferreira a , Maria Vittoria A. P. Heller a a Institute of Physics, University of S˜ ao Paulo, C. P. 66318, 05315-970 S˜ ao Paulo, S.P., Brazil b Departamento de Bioqu mica, Instituto de Qu mica, Universidade de S˜ ao Paulo, C.P. 26077, 05599-970, S˜ ao Paulo, S.P., Brazil c Instituto de Ciˆ encias Biom edicas, Universidade de S˜ ao Paulo, C.P. 11461, 05422-970, S˜ ao Paulo, S.P., Brazil Received 12 June 2000 Abstract We analyze uctuating observables of high-dimensional systems as the New York Stock Mar- ket S&P 500 index, the amino-acid sequence in the M. genitalium DNA, the maximum temper- ature of the San Francisco Bay area, and the toroidal magneto plasma potential. The probability measures of these uctuations are obtained by the statistical analysis of a rescaling combination of the rst Poincar e return time of a low-dimensional chaotic system. This result indicates that it is possible to use a measure of a low-dimensional chaotic attractor to describe a measure of these complex systems. Moreover, within this description we determine scaling power laws for average measurements of the analyzed uctuations. c  2000 Elsevier Science B.V. All rights reserved. PACS: 05.40.+j; 05.45.+b; 47.52.+j; 83.85.Ns Keywords: Chaos; Econophysics; Stock market; DNA; Turbulence; Modeling 1. Introduction It is common to come across a high-dimensional system whose unknown dynamics is the subject of dierent conjectures. For such systems, it would be of general interest to address the statistic of some uctuating measurables which contains information * Corresponding author. Fax: +55-11-38186749. E-mail address: murilo@if.usp.br (M.S. Baptista). 0378-4371/00/$ - see front matter c  2000 Elsevier Science B.V. All rights reserved. PII: S0378-4371(00)00448-9