Arnon Amir, Michael Lindenbaum
IEEE Transactions on Pattern Analysis and Machine Intelligence
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.