  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.
