DYNAMICS OF COMPOSITE SYMPLECTIC DEHN TWISTS

Wenmin Gong, Zhijing Wendy Wang, Jinxin Xue

correctmedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves that, for an A_m-chain of Lagrangian spheres and alternating-sign exponents, a suitable composition of symplectic Dehn twists has positive topological entropy by reducing to a 2D invariant subsystem (a multi-linked twist map), establishing positive Lyapunov exponents on a positive-measure set, and then lifting positivity to the ambient manifold; see the statements of Theorems 1.1 and 1.2 and their proof outline (reduction to Y and the inequality h_top(τ) ≥ h_top(τ|X) = h_top(T) ≥ h_μ(T) > 0) . The model solution adopts the same local plumbing/Weinstein reduction and relies on the same result to conclude a horseshoe (explicitly mentioned as a standard corollary in the paper) and positive entropy, and it notes exponential Floer growth consistent with Theorems 1.4–1.5 . No substantive logical conflicts were found; the approaches coincide in substance.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript establishes positive topological entropy for alternating-sign compositions of symplectic Dehn twists in A\_m configurations via a careful local reduction to a 2D subsystem and application of Pesin theory, and it complements this with Floer-theoretic growth results. The work is technically sound and clearly presented, with well-motivated connections to pseudo-Anosov dynamics. Minor additions clarifying standard consequences (horseshoe existence) and representative dependence would further strengthen readability.