E. D. Tymchatyn - Measures and topological dynamics on Menger manifolds

Joint research with H. Kato, K. Kawamura and M. Tuncali.

We study non-atomic, locally positive, Lebesgue-Stieltjes measures on compact, connected, Menger manifolds. We show that each such manifold X admits an essentially unique, normalized, non-atomic, locally positive, Lebesgue-Stieltjes measure. The set of ergodic homeomorphisms on X forms a dense G_d in the space of all measure preserving autohomeomorphisms of X in the compact open topology. In particular, there exists a topologically transitive homeomorphism on X. We also prove the existence of chaotic homeomorphisms on X.