Parametrization of small paths in real analytic geometry. (Paramétrisations de petits chemins en géométrie analytique réelle.) (French) Zbl 0852.32006

Janeczko, Stanisław (ed.) et al., Singularities and differential equations. Proceedings of a symposium, Warsaw, Poland. Warsaw: Polish Academy of Sciences, Inst. of Mathematics, Banach Cent. Publ. 33, 421-436 (1996).
This is a kind of “Puiseux with parameters” theorem, and as it is always the case with this outstanding author, his result contains almost all that has been done up to now and is more general. As usual, the proofs are deep and use the newest techniques, most of them developed by the author himself.
Such a paper is not easy to follow, but it is worth following. An unprepared reader should certainly study at least the excellent book “Géométrie algébrique réelle” by J. Bochnak, M. F. Coste-Roy and M. Coste, Springer Verlag (1987; Zbl 0633.14016), and the author’s papers in Ann. Sci. Éc. Norm. Supér., IV. Sér. 27, No. 2, 173-208 (1994; Zbl 0803.32003) and Ann. Inst. Fourier 41, No. 4, 841-866 (1992; Zbl 0782.32005).
For the entire collection see [Zbl 0840.00028].


32B20 Semi-analytic sets, subanalytic sets, and generalizations