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

Date received: October 1, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabr-13.