Newton-Puiseux approximation and Łojasiewicz exponents (Q1420216)

The authors present a process to construct what they call the Newton-Puiseux approximation of the germ \(F\) where \(F\) is a germ of real analytic, complex analytic or smooth mappings. This process either yields all common non-constant factors of the real (or complex) analytic functions \(f_1,\dots, f_n\) in a suitable neighbourhood of the origin, or else, after a finite number of steps, shows that \((0,\dots,0)\) is a common isolated zero of the functions \(f_1,\dots, f_n\). At the end, the authors apply the Newton-Puiseux approximation to obtain a formula for the Łojasiewicz exponent \(Z(F)\),