Entropy and Rotation Intervals for Circle Maps Near Saddle-node Bifurcations
by
Todd Young
Ohio University and University of Maryland

Consider a one-parameter family of C^r endomorphisms f_\lambda of the circle. Suppose that f₀ has a saddle-node periodic point and is on the boundary of an interval of phase locking. Provided f_\lambda generically unfolds f₀, then f_\lambda exhibits nontrivial behavior for \lambda > 0. We show that the topological entropy and the width of the rotation interval of f_\lambda exhibit universality with scaling laws as \lambda\searrow 0 and give estimates for each of these characteristics. The unversality and scalings depend only on f₀, not on the particular family f_\lambda which unfolds it.

Date received: March 4, 2000