METRICS AND ENTROPY FOR NONCOMPACT SPACES

We investigate Bowen's metric definition of topological entropy for ho meomorphisms of non-compact spaces. Different equivalent metrics may a ssign to the homeomorphism different entropies. We show that the infim um of the metric entropies is greater than or equal to the supremum of the measure theoretic entropies. An example shows that it may be stri ctly greater. If the entropy of the homeomorphism can vary as the metr ics vary we see that the supremum is infinity.