Entropy and rotation intervals for circle maps near saddle-node bifurcations

Consider a one-parameter family of C-T endomorphisms f(lambda) of the circl e. Suppose that f(0) is on the boundary of an interval of phase locking and that Sr generically unfolds f(0) so that f(lambda) exhibits nontrivial beh avior for lambda > 0. We show that the topological entropy and the width of the rotation interval of f(lambda) satisfy cel tain scaling laws as lambda SE arrow 0 and give estimates for each of these characteristics. These sca lings depend only on f(0,) not on the particular family f(lambda) which unf olds it. Mathematics Subject Classification (1991): 34C35,58C25.