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Middle and long distance athletics races viewed from the perspective of complexity.pdf

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Middle and long distance athletics races viewed from the perspective of complexity.pdf

ARTICLE IN PRESS Journal of Theoretical Biology 233 (2005) 191–198 /locate/yjtbi Middle and long distance athletics races viewed from the perspective of complexity Juan M. Garc?′ a-Mansoa, Juan M. Mart?′ n-Gonza′ lezb,?, Nancy Da′ vilac, Enrique Arriazad aDepartamento de Educacio′n F?′sica, Facultad de Ciencias de la Actividad F?′sica y el Deporte, Universidad de Las Palmas de Gran Canaria, 35017 Canary Islands, Spain bDepartamento de F?′sica, Universidad de Las Palmas de Gran Canaria, Edif. Ciencias Ba′sicas, 35017 Canary Islands, Spain cDepartamento de Me′todos Cuantitativos, Facultad de Ciencias econo′micas y Empresariales, Universidad de Las Palmas de Gran Canaria, 35017 Canary Islands, Spain dDepartamento de Educacio′n F?′sica, Facultad de Educacio′n F?′sica, Universidad de Playa Ancha de Ciencias de la Educacio′n, Casilla 34-V. Avenida Playa Ancha 850, Valpara?′so, Chile Received 10 May 2004; accepted 4 October 2004 Available online 18 November 2004 Abstract Middle and long distance athletics races behave as power-laws when time (or average speed) and distance are related, thus suggesting the presence of critical phenomena. Power-laws as a function of the athlete’s position in the all-time world ranking allows us to de?ne a Performance Index that reveals the existence of possible multifractal structures associated to the natural barriers to that the athletes tend in their evolution towards better results and in pursuit of world records. The new theories of self-organized critical phenomena provide an explanation for the power-law and fractal structures in systems at, or near, their critical points. In this paper we analyse the athletic races using these theories and as a result of this study a new variety of interpretations are posited. r 2004 Elsevier Ltd. All rights reserved. Keywords: Middle and long distance running; Nonlinear complex systems; Power-law; Self-organized criticality; Multifractal; Sport training. 1. Introduction This paper aims to analyse mi