Domains of analyticity for response solutions in strongly dissipative forced

We study the ordinary differential equation ɛx ̈ +x ̇ +ɛg(x)=ɛf(ωt) , where g and f are real-analytic functions, with f quasi-periodic in t with frequency vector ω . If c 0 ∈R is such that g(c 0) equals the average of f and g′(c 0) ≠ 0, under very mild assumptions on ω there exists a quasi-periodic solution close to c 0 with frequency vector ω . We show that such a solution depends analytically on ɛ in a domain of the complex plane tangent more than quadratically to the imaginary axis at the origin.