"CONNECT-THE-DOTS" TREE MAPS

Abstract

We announce the main results of work in progress on piecewise monotone models for patterns of tree maps. More precisely, we define a notion of pattern for tree maps, and given such a pattern, we construct a tree and a piecewise monotone map on this tree with the same pattern. This piecewise monotone model has the least entropy among all models exhibiting the given pattern and has "minimal dynamics". We also give a formula to compute this minimal entropy directly from the pattern. These results generalize the known results for interval maps and the results from Li & Ye [1993].