Sums of variables at the onset of chaos

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• 作者：Miguel Angel Fuentes (1) (2) (3)
  Alberto Robledo (4)
  
• 关键词：Statistical and Nonlinear Physics
• 刊名：The European Physical Journal B - Condensed Matter
• 出版年：2014
• 出版时间：February 2014
• 年：2014
• 卷：87
• 期：2
• 全文大小：423 KB
• 作者单位：Miguel Angel Fuentes (1) (2) (3)
  Alberto Robledo (4)
  
  1. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, 87501, New Mexico, USA
  2. Centro At贸mico Bariloche, Instituto Balseiro and CONICET, 8400, Bariloche, Argentina
  3. Centro de Investigaci贸n en Complejidad Social, Facultad de Gobierno, Universidad del Desarrollo, Santiago, Chile
  4. Instituto de F铆sica y Centro de Ciencias de la Complejidad, Universidad Nacional Aut贸noma de M茅xico, Apartado Postal 20-364, 01000 DF, M茅xico, Mexico
  
• ISSN：1434-6036

文摘

We explain how specific dynamical properties give rise to the limit distribution of sums of deterministic variables at the transition to chaos via the period-doubling route. We study the sums of successive positions generated by an ensemble of initial conditions uniformly distributed in the entire phase space of a unimodal map as represented by the logistic map. We find that these sums acquire their salient, multiscale, features from the repellor preimage structure that dominates the dynamics toward the attractors along the period-doubling cascade. And we explain how these properties transmit from the sums to their distribution. Specifically, we show how the stationary distribution of sums of positions at the Feigebaum point is built up from those associated with the supercycle attractors forming a hierarchical structure with multifractal and discrete scale invariance properties.