Rescaled-Expansive Flows: Unstable Sets and Topological Entropy

The paper’s Theorem D (non-periodic attractor without singularities in an R-expansive flow implies positive entropy) is proved by showing such an attractor has no R-stable/unstable points, then invoking Theorems B and C to obtain h(φ) > 0; the steps are explicit in the text and consistent with earlier results. By contrast, the model’s proof hinges on claiming the time-one map is cw-expansive on Γ; that claim is false in general because arbitrarily small orbit arcs remain uniformly small under all iterates, contradicting cw-expansiveness for homeomorphisms. Hence the model’s reasoning is flawed even though it reaches the correct conclusion.