Geodesic
The nonexistence of expansive homeomorphisms of chainable continua
Fundamenta Mathematicae, Tome 149 (1996) no. 2, pp. 119-126.

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A homeomorphism f:X → X of a compactum X with metric d is expansive if there is c > 0 such that if x, y ∈ X and x ≠ y, then there is an integer n ∈ ℤ such that $d(f^n(x),f^n(y)) > c$. In this paper, we prove that if a homeomorphism f:X → X of a continuum X can be lifted to an onto map h:P → P of the pseudo-arc P, then f is not expansive. As a corollary, we prove that there are no expansive homeomorphisms on chainable continua. This is an affirmative answer to one of Williams' conjectures.
DOI : 10.4064/fm-149-2-119-126

Hisao Kato 1

1 
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Hisao  Kato. The nonexistence of expansive homeomorphisms of chainable continua. Fundamenta Mathematicae, Tome 149 (1996) no. 2, pp. 119-126. doi : 10.4064/fm-149-2-119-126. http://geodesic.mathdoc.fr/articles/10.4064/fm-149-2-119-126/

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