Topological pressure of Cantor minimal systems within a strong orbit equivalence class

ln this paper we will show that for any Cantor minimal system (X,φ), any potential function f and any c with sup{∫ fdμ | μ is a φ-invariant probability measure on X } ≤ c ≤ ∞，there exists a Cantor minimal system (Y,ψ) such that φ and ψ are strongly orbit equivalent and the topological pressure of ψ determined by f is equal to c. If c is finite，we can take ψ as a (minimal) subshift. This result is generalization of the paper [S3]: On the subshift within strong orbit equivalence class for minimal homeomorphisms