Zeta functions and topological entropy of periodic nonautonomous dynamical systems
Let \((f_1,f_2,\dots,f_k,\dots)\) be a \(k\)-periodic (\(k\) is a positive integer) sequence of piecewise monotone maps. The paper under review extends the Artin-Mazur zeta functions to the setting of periodic sequences of maps. Although some differences with the autonomous case (\(k=1\)) appear, it is proved that the zeta function does not need to be meromorphic. The authors find sufficient conditions to guarantee that the zeta function is meromorphic and the topological entropy can be computed using the periodic points of the sequence. The positive results are proved for sequences of maps such that the so-called crossing sets \(C_{i,j}=\{ x\in [0,1]:f_i(x)=f_j(x)\}\) for \(i,j=1,\dots,k\) are finite unions of compact intervals.
scientific article; zbMATH DE number 6155678