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Measures and topological dynamics on Menger manifolds

✍ Scribed by H. Kato; K. Kawamura; H.M. Tuncali; E.D. Tymchatyn

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
318 KB
Volume
103
Category
Article
ISSN
0166-8641

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✦ Synopsis

We study nonatomic, locally positive, Lebesgue-Stieltjes measures on compact Menger manifolds and show that the set of all ergodic homeomorphisms on any compact Menger manifold X forms a dense G Ξ΄ set in the space of all measure preserving autohomeomorphisms of X with the compactopen topology. In particular, there exists a topologically transitive homeomorphism on any compact Menger manifold, which answers a question posed by several authors.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.

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