An analogue of the Misiurewicz-Przytycki theorem for several maps (Q2784525)

Let \(X\) be a compact metric space and \( f_1,f_m \) be continuous maps of \(X\) into itself which generate a semigroup \(\langle f_1,f_m\rangle\) under composition. The topological entropy of the semigroup is defined following \textit{A. Bufetov} [J. Dyn. Control Syst. 5, 137-143 (1999; Zbl 0949.37001)]. For the case of a compact smooth orientable manifold X and \(C^1\) smooth maps a lower bound for this entropy is obtained which generalizes the Misiurewicz-Przytycki theorem [\textit{M. Misiurewicz} and \textit{F. Przytycki}, Bull. Acad. Polon. Sci., Ser. Math. Astron. Phys. 25, 573-574 (1977; Zbl 0362.54037)].