On Gradient curves of an analytic function near a critical point

Collection : Lanford, Oscar Erasmus III

Auteur(e.s) : KUIPER

Date : 06/1991

Description : René 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.

Sujet(s) : COURBES

Source : M/91/36

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