Nonchaotic Stagnant Motion in a Marginal Quasiperiodic Gradient System

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dc.creatorMitsui, Takahito
dc.date2008-01-09
dc.date2008-08-25
dc.date.accessioned2026-07-07T09:57:49Z
dc.date.available2026-07-07T09:57:49Z
dc.descriptionA 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.
dc.description11pages, 5figures
dc.identifierhttps://arxiv.org/abs/0801.1370
dc.identifierhttp://arxiv.org/abs/0801.1370
dc.identifierPhysical Review E 78, 026206 (2008)
dc.identifierdoi:10.1103/PhysRevE.78.026206
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167488
dc.subjectChaotic Dynamics
dc.titleNonchaotic Stagnant Motion in a Marginal Quasiperiodic Gradient System
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