Hierarchical Expansion of Finite Discrete Dynamical Systems: A Non-Archimedean Variational Theory over Coordinate Orderings

A finite dynamical system on $\mathbb{F}_p^N$ has a functional graph and combinatorial basins, but nothing on which to run the local analysis a multiplier makes possible. We supply one. Orderings encode configurations as residue classes in $\mathbb{Z}_p$, and an exact rational interpreter over $\mat