Periodic homeomorphisms of chainable continua
Wayne Lewis (1983)
Fundamenta Mathematicae
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Wayne Lewis (1983)
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Kazuhiro Kawamura, Janusz Prajs (1991)
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A. Lelek (1970)
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Hisao Kato (1991)
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Akira Tominaga (1983)
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Judy Kennedy (1988)
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Lex Oversteegen, E. Tymchatyn (1984)
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Michel Smith (1981)
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Kazuhiro Kawamura (1991)
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F. Jones (1963)
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Christopher Mouron (2011)
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A homeomorphism h: X → X of a compactum X is expansive provided that for some fixed c > 0 and every x, y ∈ X (x ≠ y) there exists an integer n, dependent only on x and y, such that d(hⁿ(x),hⁿ(y)) > c. It is shown that if X is a solenoid that admits an expansive homeomorphism, then X is homeomorphic to a regular solenoid. It can then be concluded that a circle-like continuum admits an expansive homeomorphism if and only if it is homeomorphic to a regular solenoid.