Problem 3.4
An extended gradient conjecture
Luiz Carlos Martins Jr.
Universidade Paulista - UNIP
15091-450, S. J. do Rio Preto, SP
Brazil
Geraldo Nunes Silva
Departamento de Computacao e Estatistica
Universidade Estadual Paulista - UNESP
15054-000, S. J. do Rio Preto, SP
Brazil
1 DESCRIPTION OF THE PROBLEM
2 MOTIVATION AND HISTORY OF THE PROBLEM
3 KNOWN RESULTS AND REMARKS
BIBLIOGRAPHY
[1] F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley Inter-science, New York 1983; reprinted as vol. 5 of Classics in Applied Mathematics, SIAM, Philadelphia, PA, 1990; Russian translation, Nauka, Moscow, 1988.
[2] F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, P. R. Wolenski, Nonsmooth Analysis and Control Theory, GTM 178, New York, Springer-Verlag, 1998.
[3] F. Ichikawa, “Thom’s conjecture on singulatiries of gradient vector fields, ” Kodai Math. J. 15, pp. 134-140, 1992.
[4] K. Kurdyka, T. Mostowski, The Gradient Conjecture of R. Thom, preprint, 1996 (revised 1999). http://www.lama.univ-savoie. fr/sitelama/Membres/pages web/KURDIKA/index.html.
[5] K. Kurdyka, “On the gradient conjecture of R. Thom, ” Seminari di Geometria 1998-1999, Universitàdi Bologna, Istituto di Geometria, Di-partamento di Matematica, pp. 143-151, 2000.
[6] K. Kurdyka, T. Mostowski, A. Parusinki, “Proof of the gradient conjecture of R. Thom, ” Annals of Mathematics, 152 (2000), pp. 763-792.
[7] S. Lojasiewicz, “Une propriété topologique des sous-ensembles analy-tiques réels, ” Colloques Internationaux du C.N.R.S. #117, les équations aux dérivées partielles, Paris 25-30 juin (1962), pp. 87-89.
[8] S. Lojasiewicz, Ensembles semi-analytiques, IHES preprint, 1965.
[9] R. Moussu, “Sur la dynamique des gradients. Existence de variétés in-variants, ” Math. Ann., 307 (1997), pp. 445-460.
[10] F. Sanz, “Non oscillating solutions of analytic gradient vector fields, ” Ann. Inst. Fourier, Grenoble 48 (4) 1998, pp. 1045-1067.
[11] H. Xing Lin, Sur la structure des champs de gradients de fonctions analytiques réelles, Ph. D. Thèse, Universite Paris VII, 1992.