On Gradient curves of an analytic function near a critical point
COURBES
ANALYSE VECTORIELLE
FONCTIONS ANALYTIQUES
RenĂ© Thom [T] conjectured that a gradient curve x(t) of an analytic function on Rn, wich descends to the critical point x(?) = 0 ? Rn, called a path, has there a tangent. We prove this in case n = 3 for standard paths and standard functions.
For the remaining, rare paths and rare functions we reduce the conjecture for irreductible ? to an evident conjecture and give some arguments in favour of CRT for reductible ?. We did not succeed in elaborating these arguments to a complete proof that covers all cases.
KUIPER
M/91/36
IHES
06/1991
A4
37 f.
EN
TEXTE
PREPUBLICATION
M_91_36.pdf
1991