García-Manso Juan M, Martín-González Juan M, Dávila Nancy, Arriaza Enrique
Departamento de Educación Física, Facultad de Ciencias de la Actividad Física y el Deporte, Universidad de Las Palmas de Gran Canaria, 35017 Canary Islands, Spain.
J Theor Biol. 2005 Mar 21;233(2):191-8. doi: 10.1016/j.jtbi.2004.10.014. Epub 2004 Nov 18.
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 define 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.
当时间（或平均速度）与距离相关时，中长跑比赛呈现出幂律关系，这表明存在临界现象。作为运动员在世界历史排名中位置的函数的幂律，使我们能够定义一个表现指数，该指数揭示了与运动员在追求更好成绩和世界纪录的过程中所倾向的自然障碍相关的可能的多重分形结构的存在。自组织临界现象的新理论为处于或接近临界点的系统中的幂律和分形结构提供了解释。在本文中，我们使用这些理论分析体育比赛，并且作为这项研究的结果提出了各种各样的新解释。
