Devil's staircase in a one-dimensional mapping

T. Horiguchi and T. Morita

Physica A: Statistical Mechanics and its Applications, 1984, vol. 126, issue 3, 328-348

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.

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:126:y:1984:i:3:p:328-348

DOI: 10.1016/0378-4371(84)90205-X

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