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arXiv · 0801.1370

Nonchaotic Stagnant Motion in a Marginal Quasiperiodic Gradient System

Takahito Mitsui
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Abstract

A one-dimensional dynamical system with a marginal quasiperiodic gradient is presented as a mathematical extension of a nonuniform oscillator. The system exhibits a nonchaotic stagnant motion, which is reminiscent of intermittent chaos. In fact, the density function of residence times near stagnation points obeys an inverse-square law, due to a mechanism similar to type-I intermittency. However, unlike intermittent chaos, in which the alternation between long stagnant phases and rapid moving phases occurs in a random manner, here the alternation occurs in a quasiperiodic manner. In particular, in case of a gradient with the golden ratio, the renewal of the largest residence time occurs at positions corresponding to the Fibonacci sequence. Finally, the asymptotic long-time behavior, in the form of a nested logarithm, is theoretically derived. Compared with the Pomeau-Manneville intermittency, a significant difference in the relaxation property of the long-time average of the dynamical variable is found.

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Takahito Mitsui. 2008-08-25. Nonchaotic Stagnant Motion in a Marginal Quasiperiodic Gradient System. https://doi.org/10.1103/physreve.78.026206

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