Inégalité de Lojasiewicz en géométrie pfaffienne

Illinois Journal of Mathematics

Volumn 44, Issue 4, 2000, Pages 889-900

  Lion, Jean Marie ^a  

^a UNIVERSITÉ DE BOURGOGNE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012635902     PISSN: 00192082     EISSN: None     Source Type: Journal    
DOI: 10.1215/ijm/1255984699     Document Type: Article

References (28)

1. J. M. Aroca, H. Hironaka et J. L. Vicente, Desingularization theorems, Mem. Mat. Inst. Jorge Juan, no. 30, CSIC, Madrid 1977; The theory of the maximal contact, ibid, no. 29, 1975.
2. J. M. Aroca, H. Hironaka et J. L. Vicente, Desingularization theorems, Mem. Mat. Inst. Jorge Juan, no. 30, CSIC, Madrid 1977; The theory of the maximal contact, ibid, no. 29, 1975.
3. J. Bochnak, M. Coste et F. Roy, Géométrie algébrique réelle, Erg. Mat. (3), no. 12, Springer-Verlag, New York, 1987.
4. F. Cano, J.-M. Lion et R. Moussu, Frontière d'une hypersurface pfaffienne, Ann. ENS 28 (1995), 591-646.
5. J. Denef, L. van den Dries, p-adic and real subanalytic sets, Ann. of Math. 128 ( 1988), 79-138.
6. L. van den Dries et C. Miller, Geometric categories and o-minimal structures, Duke Math. J. 84 (1996), 497-540.
7. L. van den Dries, A. Macintyre et D. Marker, The elementary theory of restricted analytic fields with exponentiation, Ann. of Math. 140 (1994), 183-205.
8. L. van den Dries, Tame topology and o-minimal structures, London. Math. Soc. Lecture Note Ser., no. 248, Cambridge Univ. Press, Cambridge, 1998.
9. _, Bounding the rate of growth of solutions of algebraic differential equations and exponential equations in Hardy fields, preprint, 1982.
10. S. Denkowska et J. Stasica, Ensemble sous-analytiques à la polonaise, preprint, 1985.
11. A. M. Gabrielov, Projections of semi-analytic sets, Funct. Anal. Appl. 2 (1968), 282-291.
12. A. M. Gabrielov, Complements of subanalytic sets and existential formulas for analytic functions, Invent. Math. 125 (1996), 1-12.
13. A. M. Gabrielov, Multiplicities of Pfaffian intersections, and the Lojasiewicz inequality, Selecta Math. (N. S.) 1(1995), 113-127.
14. D. Grigoriev, Deviation theorems for pfaffian sigmoids, Algebra i Analiz 6 (1994), 127-131.
15. _, Deviation theorems for solutions of linear ordinary differential equations and applications to parallel complexity of sigmoids, Algebra i Analiz 6 (1994), 110-126.
16. H. Hironaka, Introduction to real-analytic sets and real-analytic maps, Istituto Matematico "L. Tonelli", Pisa, 1973.
17. A. G. Khovanskii, Real analytic varieties with the finitness property and complex abelian integrals, Funct. Anal. Appl. 18 (1984), 119-127.
18. S. Lojasiewicz, Ensembles semi-analytiques, preprint, IHES, 1965.
19. J.-M. Lion et J.-P. Rolin, Volumes, Feuilles de Rolle de Feuilletages analytiques et Théorème de Wilkie, Annales de Toulouse 7 (1998), 93-112.
20. _, Théorème de préparation pour les fonctions logarithmico-exponentielles, Ann. Inst. Fourier 47 (1997), 859-884.
21. _, Théorème de Gabrielov et fonctions log-exp-algébriques, CRAS 324 (1997), 1027-1030.
22. J.-M. Lion et P. Speissegger, The pfaffian closure: analytic stratifications, preprint (version de mars 1999).
23. R. Moussu et C. A. Roche, Théorie de Hovanskii et problème de Dulac, Invent. Math. 105 (1991), 431-441.
24. A. Parusiński, Lipschitz stratification of subanalytic sets, Ann. ENS 27 (1994), 661-996.
25. M. Rosenlicht, The rank of a Hardy field, Trans. Amer. Math. Soc. 280 (1983), 659-671.
26. P. Speissegger, The Pfaffian closure of an o-minimal structure, J. Reine Angew. Math. 508 (1999), 189-211.
27. J.-C. Tougeron, Inégalités de Lojasiewicz globales, Ann. Inst. Fourier 41 (1991), 841-866.
28. A. Wilkie, Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function, J. Amer. Math. Soc. 9 (1996), 1051-1094.