Santiago Length Dynamical System to Predict Message Inflation and Size Buffers in IIoT Pipelines

Abstract

We propose the Santiago Dynamical System (SDS) as a unifying formulation of discrete dynamics on N generated by a coding and an observable. The central case studied in this work is the length SDS, where the observable is the length of a word α(n) over an alphabet Σ, giving rise to the iteration nk+1 = α(nk) . This perspective connects functional graphs on N with symbolic dynamics, coding theory, and Lyapunov-type potential methods. Universal structural properties are presented, including contraction/expansion criteria and a methodological framework to characterize attractors, basins, and iterative complexity in classes of natural codings. Finally, conjectures are formulated concerning small attractors and iterated-logarithmtype convergence in compact codings.