Domains of analyticity for response solutions in strongly dissipative forced systems

We study the ordinary differential equation epsilon<(x)double over dot> + <(x)over dot> + epsilon g(x) = epsilon f(omega t), where g and f are real-analytic functions, with f quasi-periodic in t with frequency vector omega. If c(0) is an element of R is such that g(c(0)) equals the average of f and g'(c(0)) not equal 0, under very mild assumptions on omega there exists a quasi-periodic solution close to c(0) with frequency vector omega. We show that such a solution depends analytically on epsilon in a domain of the complex plane tangent more than quadratically to the imaginary axis at the origin. (C) 2013 AIP Publishing LLC.