On indecomposability and composants of chaotic continua, II

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(fn(x),fn(y))>c. A homeomorphism f:X→X is continuum-wise expansive if there is c>0 such that if A is a nondegenerate subcontinuum of X, then there is an integer n∈Z such that . Note that every expansive homeomorphism is continuum-wise expansive, but the converse assertion is not true. In this paper, we define the notion of closed subsets having uncountable handles and we prove that if f:X→X is a continuum-wise expansive homeomorphism of a continuum X and X does not contain any subcontinuum having uncountable handles, then each minimal chaotic continuum of f is indecomposable. As a corollary, we obtain that if X is a k-cyclic continuum and X admits a continuum-wise expansive homeomorphism f, then each minimal chaotic continuum of f is indecomposable.