It is well known that periodic orbits with any period can appear in sequential dynamical systems over undirected graphs with a Boolean maxterm or minterm function as global evolution operator. Indeed, fixed points cannot coexist with periodic orbits of greater periods, while periodic orbits with different periods greater than 1 can coexist. Additionally, a fixed point theorem about the uniqueness of a fixed point is known. In this paper, we provide an $m$-periodic orbit theorem (for $m>1$) and we give an upper bound for the number of fixed points and periodic orbits of period greater than 1, so completing the study of the periodic structure of such systems. We also demonstrate that these bounds are the best possible ones by providing examples where they are attained.

众所周知，具有周期的周期轨道可以在具有布尔最大项或最小项函数作为全局演化算子的​​无向图上的顺序动力学系统中出现。实际上，固定点不能与更大周期的周期轨道共存，而不同周期大于1的周期轨道可以共存。另外，关于定点唯一性的不动点定理是已知的。在本文中，我们提供了$米$-周期轨道定理（用于 $米>\mathrm{1个}$），并给出不大于1的不动点和周期轨道的上限，因此完成了对此类系统的周期结构的研究。我们还通过提供达到目标的示例来证明这些边界是可能的最佳边界。