Markov partitions for nonhyperbolic systems (Q2785860)

It is known [\textit{Ya. Sinai}, Funct. Anal. Appl. 2, 245-253 (1968); translation from Funkts. Anal. Prilozh. 2, No. 3, 70-80 (1968; Zbl 0194.22602)] that for a diffeomorphism \(f\) hyperbolic on a closed invariant set \(N\) there is a Markov partition which induces a conjugacy between the restriction \(f|_N\) and a sub-shift of finite type. By using the Conley index, \textit{K. Mischaikow} and \textit{M. Mrozek} [ Japan J. Ind. Appl. Math. 12, No. 2, 205-236 (1995; Zbl 0840.58033)] received a similar result when the smoothness of \(f\) is lost. They proved that if some cohomological conditions hold then there are \(d>0\) and a semi-conjugacy taking \(f^d|_N\) on sub-shift of finite type. The author gives an extension of the notion of Markov partition for discrete dynamical systems on locally metric spaces. The main result of the article is an analog of the mentioned result on semi-conjugacy under more natural algebraic conditions. There are two applications.