The classification of circle-like continua that admit expansive homeomorphisms

• Autorzy: Christopher Mouron
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54F15: Continua and generalizations
• 37B45: Continua theory in dynamics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 211
• Numer: 2
• Strony: 101-133

Daty

wydano

2011

Twórcy

autor

Christopher Mouron

• Department of Mathematics and Computer Science, Rhodes College, Memphis, TN 38112, U.S.A.

Identyfikatory

DOI

10.4064/fm211-2-1