Topological entropy of transitive maps of a tree

Let T be a tree, End(T) be the number of ends of T and let L(T) be the infimum of topological entropies of transitive maps of T. We give an elementary approach to the estimate that L(T) greater than or equal to (1/End(T)) log2. We also divide the set of all trees (up to homeomorphisms) into pairwise disjoint subsets P(i), i is an element of {0} boolean OR N and prove that L(T) = (1/(End(T) - i))log2 if T is an element of P(i) with i = 0, i, and L(T) less than or equal to (respectively =) (1/(End(T) - i))log2 if T is an element of P(i) (respectively T is an element of P'(i)) with i greater than or equal to 2, where P'(i) is an infinite subset of P(i). Furthermore, we show that there is a tree T such that the topological entropy of each transitive map of T is larger than L(T), and hence disprove a conjecture of Alseda et al (1997).