Measures and topological dynamics on Menger manifolds
The authors study Menger manifolds from the viewpoint of dynamical systems. After some basic facts on Menger manifolds presented in the first section, in Section 2 the authors describe two ways to construct nonatomic, locally positive, Lebesgue-Stieltjes measures on compact Menger manifolds. Section 3 is devoted to the proof of the ``uniqueness'' of the Lebesgue-Stieltjes measure on any compact Menger manifold, next this result is applied in Section 4 to prove that the set of all ergodic homeomorphisms on any compact Menger manifold \(X\) forms a dense \(G_{\delta}\) set in the space of all measure preserving autohomeomorphisms of \(X\) with the compact-open topology. Finally, in Section 5 the authors prove the existence of homeomorphisms which are chaotic in the sense of Devaney as well as everywhere chaotic in the sense of Li-Yorke.
scientific article; zbMATH DE number 1454825