On homeomorphisms with Markov partitions (Q1099839)

Consider a dynamical system generated by a homeomorphism f of a compact metric space (X,d). The author proves the following theorem. Suppose that (i) for any \(\epsilon >0\) there exists \(\delta >0\) such that every \(\delta\)-pseudo-orbit is \(\epsilon\)-traced by an orbit; (ii) there exists \(a>0\) such that d(f n(x),f n(y))\(\leq a\) for all \(n\in {\mathbb{Z}}\) implies \(x=y\). Then there exist Markov partitions with arbitrary small diameters.