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

Mendoza Delgado R.S.; Mendoza Arenas R.D.; Rojas Orbegoso J.L.; Farfán Aguilar J.A.; Morales Chalco O.R.; La Chira Loli M.B.; Arbañil Rivadeneira R.O. · Proceedings of the LACCEI international Multi-conference for Engineering, Education and Technology (2026) · DOI: 10.18687/laccei2026.1.1.502

Resumen

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-logarithm-type convergence in compact codings.

Instituciones: Universidad Nacional Mayor de San Marcos; Universidad Autónoma del Perú; Universidad Nacional del Callao