Abstract
We study the combinatorial structure of periodic orbits of nonautonomous difference equations 𝒳βββ = 𝒇β(𝒳β) in a periodically fluctuating environment. We define the ΣΆ-set to be the set of minimal periods that are not multiples of the phase period. We show that when the functions 𝒇β are rational functions, the ΣΆ-set is a finite set. In particular, we investigate several mathematical models of single-species without age structure, and find that periodic oscillations are influenced by periodic environments to the extent that almost all periods are divisors or multiples of the phase period.
