Markov Maps On The Circumference Of The Inverse Limit Space

In §0 we introduce the significance of inverse limit spaces research, some known results on inverse limit spaces on intervals or graphs and the main results of our research. In §1 we introduce as preparative knowledge the basic continuum theory of inverse limit spaces. In §2 we define Markov maps on S~1 through lifts on R while the Markov maps which take an arc between two adjacent partition points onto the circle and make it surround the circle several times are taken into special consider. We also give an important theorem on a kind of inverse sequences of Markov maps on the circle with respect to a fixed partition. In §3 we prove that two sequences of Markov maps on the circle generated homeomorphic inverse limit spaces if each pair of the bounding maps with the same subscript are of the same Markov type with respect to a fixed arrangement of the two partitions. Here we allow the bounding maps to have infinitely many horizontal intervals. The relative conclusions are extended to the inverse limit spaces of interval Markov maps.