Periodic Orbits of Continuous Mappings of the Circle

Louis Block
1980 Transactions of the American Mathematical Society  
Let / be a continuous map of the circle into itself and let P(f) denote the set of positive integers n such that/has a periodic point of period n. It is shown that if 1 G P(f) and n G P(f) for some odd positive integer n then for every integer m > n, m G P(f). Furthermore, if P(f) is finite then there are integers m and n (with m > 1 and n > 0) such that P(f) = [m, 2 • m, 4 • m, 8 • m.2" • m).
doi:10.2307/1998021 fatcat:rewhnghnkjcxbgfhaoxccprqci