2011.14002
Effects of local mutations in quadratic iterations
Anca Rǎdulescu, Abraham Longbotham
correctmedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves that M = 1 + sqrt(1 + |c0| + |c1|) is an escape radius for the radially interpolated map f, splitting the argument into annulus and interior/exterior regions (Theorem 2.5). The model’s solution presents the same core inequality in a uniform way by bounding w(z) ∈ conv{c0,c1}, arriving at the identical threshold and conclusion. The model also notes a simple tightening (replace |c0| + |c1| by max{|c0|,|c1|}), which the paper does not exploit but does not contradict.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper correctly establishes a global escape radius for a radially interpolated, non-analytic mutation of quadratic dynamics and supports it with extensive numerics. The main argument is sound and clear. Minor issues include an unnecessary side-condition in one lemma and the use of a conservative constant where a sharper choice is immediate. With small clarifications and polish, the contribution is solid and publishable.