Expansive homeomorphisms and indecomposable subcontinua

Abstract

A continuum X is k-cyclic if given any ε>0, there is a finite open cover U of X such that mesh(U)<ε and the nerve N(U) is has at most k distinct simple closed curves. A homeomorphism h:X→X is called expansive provided for some fixed ε>0 and every x,y∈X there exists an integer n such that d(hn(x),hn(y))>ε. We prove that if X is a k-cyclic continuum that admits an expansive homeomorphism, then X must contain an nondegenerate indecomposable subcontinuum.