Measures and topological dynamics on Menger manifolds
by
E.D. Tymchatyn
University of Saskatchewan
Coauthors: H.Kato, K.Kawamura, H.M.Tuncali

We study nonatomic, Lesbesgue-Stieltjes measures on compact Menger manifolds X.We show that the set of all ergodic homeomorphisms on X is a dense Gdelta set in the space of all measure preserving autohomeomorphisms of X with the compact-open topology.In particular there exists a topologically transitive homeomorphism of X.We also prove the existence of homeomorphisms that are chaotic in the sense of Devaney as well as everywhere chaotic in the sense of Li-Yorke.

Date received: February 9, 1998