Abstract
AbstractLetXbe a compact Hausdorff space,f∈C0(X, X) andA⊂Xa minimal set off. We first introduce a new topological invariant, the D-function of a minimal set, by the investigation of the decomposition of the minimal set A under the action offn,n∈N. Then important properties about the invariant and the existence of minimal set with a given D-function in some subshift of finite type are discussed. Finally Sharkovskii's theorem is generalized to minimal sets of continuous mappings from the interval into itself.
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