Combinatorial vs. Classical Dynamics: Recurrence

The paper’s Theorem 4.6 is stated with precise hypotheses (a)–(f) and proved by embedding the semiflow on the isolating block into a compact ANR with a global section, then invoking McCord–Mischaikow–Mrozek’s result to force a periodic orbit; the construction (Urysohn map to S1, adjunction, and global section) is complete and internally consistent with the preliminaries on isolating blocks and brick paths. By contrast, the candidate proposes an alternative Lefschetz–Poincaré-return approach but leaves the crucial fixed-point index/Lefschetz-number computation and continuity of the return map unproved; thus the model’s solution is only an outline and is incomplete.