Local monomialization of generalized analytic functions

Generalized power series extend the notion of formal power series by considering exponents of each variable ranging in a well ordered set of positive real numbers. Generalized analytic functions are defined locally by the sum of convergent generalized power series with real coefficients. We prove a local monomialization result for these functions: they can be transformed into a monomial via a locally finite collection of finite sequences of local blowings-up. For a convenient framework where this result can be established, we introduce the notion of generalized analytic manifold and the correct definition of blowing-up in this category.