Spectral invariants of periodic nonautonomous discrete dynamical systems

For an interval map, the poles of the Artin–Mazur zeta function provide topological invariants which are closely connected to topological entropy. It is known that for a time-periodic nonautonomous dynamical system F with period p, the p  -th power [ζF(z)]p[ζF(z)]p of its zeta function is meromorphic in the unit disk. Unlike in the autonomous case, where the zeta function ζf(z)ζf(z) only has poles in the unit disk, in the p  -periodic nonautonomous case [ζF(z)]p[ζF(z)]p may have zeros. In this paper we introduce the concept of spectral invariants of p  -periodic nonautonomous discrete dynamical systems and study the role played by the zeros of [ζF(z)]p[ζF(z)]p in this context. As we will see, these zeros play an important role in the spectral classification of these systems.