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

E. D. TYMCHATYN, University of Saskatchewan, Saskatoon, Saskatchewan  S7N 5E6, Canada
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 Gd 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.


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