We compute the Łojasiewicz exponent of $f=(f_1,\ldots,f_n)\colon \Bbb R^2\to\Bbb R^n$ via the real approximation of Puiseux"s expansions at infinity of the curve $f_1\ldots f_n=0$. As a consequence we construct a collection of real meromorphic curves which provide a testing set for properness of $f$ as well as a condition, which is very easy to check, for a local diffeomorphism to be a global one.
"A formula for the Łojasiewicz exponent at infinity in the real plane via real approximations." Hokkaido Math. J. 38 (3) 417 - 425, August 2009. https://doi.org/10.14492/hokmj/1258553971