On Bifurcation Sets for Symbolic Dynamics in the Milnorthurston World

We show the continuity of the topological entropy for the MilnorThurston world of interval maps and we compute the minimum and the maximum values for the entropy of a maximal sequence of any given period. We also study (fractal) geometric properties of the bifurcation set in the parameter space and in the associated phase spaces ?[a, b], and we compare these results with the previously known results about the lexicographic world of interval maps (related to Lorenz-like maps). © 2012 World Scientific Publishing Company.