Entropy estimates for transitive maps on trees

If X is a space, define L(X) to the the infimum of all possible values h(f) , where h(f) denotes the topological entropy off; and f ranges over all tra nsitive functions on X. Various lower and upper bounds are given for L(T) i n the case for which T is a tree, which provides an exact value of L(T) for a large class of trees. We also examine the analogous problem when f is re quired to fix the endpoints of the tree. (C) 2001 Elsevier Science Ltd. All rights reserved.