2010.15231
Measure, dimension, and complexity of escape in open Hamiltonian systems
Vitor M. de Oliveira, Matheus S. Palmero, Iberê L. Caldas
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper states the key properties (normalization of the mean escape measure, De2 ≤ D, c ≤ 1 with an extreme-case description, and invariance of De2 under axis normalizations) but largely without proofs. The model provides clean, standard proofs and sharper equality conditions. There is a mild ambiguity in the paper about normalization when restricting to a subregion V, but it does not contradict the model’s arguments and can be fixed with a clarifying assumption.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The manuscript presents a practical finite-time framework for quantifying escape dynamics and demonstrates it convincingly on two representative systems. The concepts are sound and the results useful. A few statements (e.g., De2 ≤ D and scaling invariance) are asserted without proof; brief arguments or citations would improve rigor. Clarifying normalization when restricting to subregions would also strengthen the presentation.