Chain recurrence in multidimensional time discrete dynamical systems (Q946971)

Expansive homeomorphisms with certain shadowing properties are said to be topologically Anosov (TA). \textit{R. Bowen}, in generalizing the smooth case of Smale's Spectral Decomposition Theorem [Dyn. Syst., Proc. Symp. Univ. Warwick 1973/74, Lect. Notes Math. 468, 35--36 (1975; Zbl 0327.58010)], showed that the set of non-wandering points of a TA map \(f\) can be decomposed into a disjoint union of closed invariant sets \(R_1,\dots, R_l\) such that \(|R_i\) is topologically transitive, \(i= 1,\dots, l\). In this paper the author considers \(d\)-dimensional systems and the main result is a multidimensional version of Bowen's Spectral Decomposition Theorem for such systems. Problems of expansivity and pseudo-orbit tracing (shadowing) are emphasized.