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. 
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
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