Topological entropy of the induced maps of the inverse limits with bonding maps

We generalize a result of Bowen by showing that the topological entropy of the induced map of the inverse limit space with bonding maps is equal to the limit of the topological entropy of the original maps. As an application we prove that the topological entropy of each induced homeomorphism of a hereditarily decomposable chainable continuum is zero and then generalize some known result of Barge and Martin.