THE FULL PERIODICITY KERNEL FOR SIGMA-MAPS

[摘要] Let sigma be the topological space formed by the points (x, y) of R2 such that either x2 + y2 = 1, or 0 less-than-or-equal-to x less-than-or-equal-to 2 and y = 1. A sigma map f is a continuous self-map of sigma having the branching point (0, 1) as a fixed point. We denote by Per(f) the set of periods of all periodic points of f, and by N the set of positive integers. We prove that if f is a sigma map and {2, 3, 4, 5, 7} subset-or-equal-to Per(f), then Per(f) = N. Conversely, if S subset-or-equal-to N is a set such that for every sigma map f S subset-or-equal-to Per(f) implies Per(f) = N, then {2, 3, 4, 5, 7} subset-or-equal-to S. (C) 1994 Academic Press, Inc.

[发布日期] 1994-05-01