We show how a generalization of continued fractions can be used to develop a renormalization-group formalism to study the behavior of maps of the two-torus. Such maps may mimic the universal behavior of dynamical systems with three mutually incommensurate frequencies. Numerical evidence indicates that "chaos" may occur in maps which are invertible. While we do not see scaling at chaos onset, subcritical scaling is observed and explained by the number theory.
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Kim et al. (1985) studied this question.
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