A SURVEY ON THE TOPOLOGICAL ENTROPY OF CUBIC POLYNOMIALS

The survey states exactly the identities the model proves—namely ℓ(f^n)=1+∑_{k=0}^{n-1}s(k), the recursion s_i^{(n)}=1+∑_{k=0}^{n-1}s(k)−S_i^{(n)}, and hence ℓ(f^n)=(s(n)+S(n))/l—and uses the same “bad symbols” correction S_i^{(n)} based on min–max data; see equations (2.11), (2.13), (2.15), and (2.16) in the paper . The model’s argument matches the paper’s counting idea (count intersections per lap and subtract two per ‘bad’ extremum) and adds a clear justification for ℓ(f^n)=1+∑ s(k) via first-entry to the critical set. The stopping rule the model mentions is the same as the paper’s criterion |(1/n)log ℓ(f^n)−(1/(n−1))log ℓ(f^{n−1})|<ε . Minor textual slips in the survey (e.g., calling y=c_i a vertical line) do not affect correctness; the model uses the correct geometry (horizontal line y=c_i).