LI–YORKE AND DEVANEY CHAOTIC UNIFORM DYNAMICAL SYSTEMS AMONGST WEIGHTED SHIFTS

The paper proves, over a finite field, the equivalence among sensitivity, strong sensitivity, existence of a forward-infinite nonzero-weighted ϕ-orbit, existence of a scrambled pair, and Li–Yorke chaos (Theorem 3.8), and also characterizes Devaney chaos via topological transitivity and the condition that ϕ is injective with no periodic points and all weights invertible (Theorem 5.2), with dense periodic points characterized in Theorem 4.1. These statements and their proofs are self-consistent and correct in the paper’s framework . The model reproduces all stated equivalences with a largely independent, sound approach (notably, a clean conjugacy to the one-sided shift to build an uncountable scrambled set). One minor gap appears in Part B, case (b) (non-injectivity of ϕ): the open-set obstruction they choose implicitly relies on the “no-zero-weights” subcase; this is harmless because the “zero-weight” obstruction is already treated separately in case (a). With that clarification, the model’s proof aligns with the paper’s conclusions.