The nonexistence of expansive homeomorphisms of chainable continua

• Autorzy: Hisao Kato
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54H20: Topological dynamics
• 54F50: Spaces of dimension ≤ 1 ; curves, dendrites
• 54B20: Hyperspaces
• 54E40: Special maps on metric spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1996
• Tom: 149
• Numer: 2
• Strony: 119-126

Daty

wydano

1996

otrzymano

1994-07-19

otrzymano

1995-08-09

Twórcy

autor

Hisao Kato

• Institute of Mathematics, University of Tsukuba, Ibaraki, 305 Japan

Bibliografia

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