A Structural Exclusion Criterion for Positive Accumulated Drift in Discrete Dynamical Systems

This article introduces a structural exclusion criterion for positive accumulated drift in discrete dynamical systems.Using logarithmic potentials and telescopic averaging, we prove that if no sub-dynamics exhibits positive mean drift and no residual subset accumulates positive drift, then the global system cannot exhibit sustained growth.The result provides a general impossibility principle applicable to discrete iterative processes, including Collatz-type dynamics.