MONOTONICITY PROPERTIES OF SOME SKEW TENT MAPS

We investigate properties of monotonicity of kneading sequences and topological entropy for some unimodal maps of the interval, called skew tent maps given by the formula [GRAPHICS] when the parameters belong to the region D1 = {lambda, mu)[lambda less-than-or-equal-to 1, mu > 1} The case lambda greater-than-or-equal-to 1 has been studied in [M-V] and the authors proved that kneading sequences and entropy are strictly increasing functions of lambda and mu. Here we prove, when lambda < 1, that kneading sequences and entropy are increasing and we identify some regions where these functions of lambda and mu are constant. We prove also that the set of (lambda, mu) where the kneading sequences is a primary itinerary M is the graph of a decreasing function lambda = beta(M) (mu) as in [M-V].