Gevrey estimates for asymptotic expansions of tori in weakly dissipative systems

The paper proves two key facts for conformally symplectic maps (including the dissipative standard map): (i) the existence/uniqueness (under normalization) of formal Lindstedt series with truncation error bounded by C_N|ε|^{N+1} (Theorem 20), and (ii) Gevrey bounds with optimal order 2τ/α for the coefficients (Main Lemma 22) . In the standard-map model, the setup and order-by-order equations are derived explicitly in Appendix A (e.g., (A.1)–(A.5)) . The candidate solution reproduces these two conclusions for the same model by a direct order-by-order Lindstedt construction, balancing two cohomological inversions per order against the ε^α feedthrough to obtain the Gevrey exponent σ=2τ/α, and giving the standard O(|ε|^{N+1}) truncation error; this matches the paper’s results. The candidate’s argument differs in technique from the paper’s Newton-on-power-series approach (Sections 3–6, with set G and degree control) , but is mathematically consistent after minor bookkeeping fixes (notably, splitting the strip-width loss across the two inversions and aligning the normalization with the paper’s).