Bowen-Franks groups of reducible bimodal subshifts of finite type
Here, bimodal maps are considered. It is assumed that the critical points are periodic. Hence, using a suitable partition into intervals, the bimodal map has the Markov property, and therefore it is conjugate to a subshift of finite type. From the transition matrix one can calculate the Bowen-Franks group of the map. In [\textit{N.~Martins}, \textit{R.~Severino} and \textit{J.~Sousa Ramos}, J. Difference Equ. Appl. 9, 423--433 (2003; Zbl 1018.37008)], an explicit formula for the Bowen-Franks group involving the bimodal kneading pair of the map has been derived. However, if the period of the critical points is large, long calculations are required to determine the Bowen-Franks group. Given two bimodal kneading pairs the *-product of these pairs was introduced in the paper of \textit{J.~P.~Lampreia}, \textit{R.~Severino} and \textit{J.~Sousa Ramos} [Grazer Math. Ber. 346, 245--254 (2004; Zbl 1061.37008)]. This product is again a bimodal kneading pair. The main result of the present paper provides a formula to calculate the Bowen-Franks group, if the kneading pair of the map can be written as the *-product of two kneading pairs.
scientific article; zbMATH DE number 5016224
scientific article