An approach to renormalization on the n-torus

The coding theory of rotations (by inspecting closely their relation to flows) and the continued fractions algorithm (by considering even two-coloring of the integers with a given proportion of, say, blue and red) are revisited. Then, even n-coloring of the integers is defined. This allows one to code rotations on the (n - 1)-torus by considering linear flows on the n-torus and yields a simple geometric approach to renormalization on tori by first return maps on the coding regions. © 1991 American Institute of Physics.