Coding rotations on intervals
Abstract
We show that the coding of rotation by α on m intervals with rationally independent lengths can be recoded over m Sturmian words of angle α. More precisely, for a given m an universal automaton is constructed such that the edge indexed by the vector of values of the ith letter on each Sturmian word gives the value of the ith letter of the coding of rotation.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.