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Devil's staircase in a one-dimensional mapping

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  • Horiguchi, T.
  • Morita, T.

Abstract

We give a one-dimensional mapping which is a simple example that the periodic orbits show an arithmetic furcation as a function of a parameter characterizing the mapping. The mapping is a piecewise linear function which consists of three parts, that is, a line with slope 1, a line with slope 0 and a line with slope a>1. When the frequency is defined by the ratio of the number of times of visiting the lines with slope a and with slope 0 within a period to the period, the frequency takes on the elements of Farey's set and behaves as a complete devil's staircase as a function of a parameter.

Suggested Citation

  • Horiguchi, T. & Morita, T., 1984. "Devil's staircase in a one-dimensional mapping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 126(3), pages 328-348.
    • Handle: RePEc:eee:phsmap:v:126:y:1984:i:3:p:328-348
    DOI: 10.1016/0378-4371(84)90205-X
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    References listed on IDEAS

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    1. Nikos Alexandratos & Jelle Bruinsma & Janos Hrabovszky, 1982. "Power inputs from labour, draught animals and machines in the agriculture of the developing countries," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 9(2), pages 127-155.
    2. Morita, T., 1983. "Free energy of the random Ising model in terms of the magnetizations of sites," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(1), pages 143-152.
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