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Emergence of self-similarity in football dynamics

The European Physical Journal B volume 87, Article number: 41 (2014) Cite this article

An Erratum to this article was published on 02 April 2014

Abstract

The multiplayer dynamics of a football game is analyzed to unveil self-similarities in the time evolution of player and ball positioning. Temporal fluctuations in both the team-turf boundary and the ball location are uncovered to follow the rules of fractional Brownian motion with a Hurst exponent of H ~ 0.7. The persistence time below which self-similarity holds is found to be several tens of seconds, implying a characteristic time scale that governs far-from-equilibrium motion on a playing field.

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Authors and Affiliations

  1. Graduate School of Education, University of Yamanashi, 4-4-37, Takeda, Kofu, 400-8510, Yamanashi, Japan

    Akifumi Kijima

  2. Division of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo, 060-8628, Hokkaido, Japan

    Keiko Yokoyama

  3. Japan Society for the Promotion of Science, 5-3-1, Koujimachi, Chiyoda-ku, 102-0083, Tokyo, Japan

    Keiko Yokoyama

  4. Department of Environmental Sciences & Interdisciplinary Graduate School of Medicine and Engineering, University of Yamanashi, 4-4-37, Takeda, Kofu, 400-8510, Yamanashi, Japan

    Hiroyuki Shima

  5. Research Center of Health, Physical Fitness and Sports & Department of Psychology and Human Developmental Sciences, Nagoya University, Chikusa, 464-8601, Nagoya, Japan

    Yuji Yamamoto

Authors
  1. Akifumi Kijima
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  2. Keiko Yokoyama
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  3. Hiroyuki Shima
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  4. Yuji Yamamoto
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Correspondence to Hiroyuki Shima.

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Kijima, A., Yokoyama, K., Shima, H. et al. Emergence of self-similarity in football dynamics. Eur. Phys. J. B 87, 41 (2014). https://doi.org/10.1140/epjb/e2014-40987-5

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  • DOI: https://doi.org/10.1140/epjb/e2014-40987-5

Keywords

  • Statistical and Nonlinear Physics