Lemmass A and B for sub-Pfaffian sets

• Autorzy: Hajto, Z.
• Języki publikacji: EN

Abstrakty

EN

In this paper we prove two fundamental lemmas of sub-Pfaffian geometry which are counterparts of Lemmas A and B for subanalytic sets [4]. We use a generalized version of the Tangent Mapping Theorem [2], following our program announced in [11].

Słowa kluczowe

PL

funkcje wielu zmiennych zespolonych; przestrzeń analityczna; stratyfikacja; układ Pfaffa; zbiór semianalityczny

EN

Pfaffian systems; semianalytic sets; stratifications

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 4
• Strony: 325--336
• Opis fizyczny: Bibliogr. 32 poz.

Twórcy

autor

Hajto, Z.

• Institut of Mathematics, University of Agriculture, Królewska 6, 30-045 Kraków, Poland,

Bibliografia

• [1] V. I. Arnold, Sur quelques problémies de la théorie des systémes dynamiques, Journées X UPS 1994, Centre de Mathématiques, École Polytechnique, (Septembre 1994).
• [2] A. B. Cabello Pardos, Z. Hajto, Stratifications adapted to finite families of differential 1-forms, (Pfaffian geometry - part one), Revista Matenmitica de la Universidad Complutense dc Madrid, 8 (199.5) 269-292.
• [3] F. Cano, J. M. Lion, R. Moussu,Frontiére d'une hypersurface pfaffienne, Ann. scient. Ec. Norm. Sup., 28 (1995) 591-646.
• [4] Z. Denkowska, S. Lojasiewicz, J. Stasica, Certaines propriétés élémentaires des ensembles sous-analytigues, Bull. Acad. Polon. Sci., Sèr. Sci. Math., XXVII (7-8) (1979) 529-536.
• [5] Z. Denkowska, S. Łojasiewicz, .J. Stasica, Sur le théorème du complementaire pour les ensembles sous-analytigues, Bull. Acad. Polon. Sci., Sèr. Math., XXVII (7-8) (1979) 537-539.
• [6]. van den Dries, Remarks on Tarski's problem concerning (R,+, exp) in: Logic Colloquium 1982, North-Holland, (1984) 97-121.
• [7] L. van den Dries, Tarski's problem and Pfaffian functions, in: Logic Colloquium 1984, North-Holland (1986) 59-90.
• [8] L. van den Dries, C. Miller, On the real exponential field with restricted analytic functions, Israel J. Math. 85 (1994) 19-56.
• [9] A, M. Gabrielo v, Projections of sernianalytic sets, Fama. Anal. Appl., 2 (1968) 282-291.
• [10] Z. Hajto, On the Gabrielov theorem for sub-Plaffian sets, Real Analytic and Algebraic Geometry, ed.:F. Broglia, M. Galbiati, A. Tognoli, Walter de Gruyter, (1995) 149-160.
• [11] Z. Hajto, The Gabrielov theorem for sub-Pfaffiansets, Tagungsbericht 22/1993, Mathernatisches Forschungsinstitut Oberwolfach, (1993), 9-10.
• [12] Z. Hajto , Sub-Pfaffian sets and a generalization of Wilkie's theorem, to be pu Wished.
• [13] A. G. Hovanskiii, On a class of systems of transcendental equations, Sov. Math. Dokl., 22 (1980) 762-765.
• [14] A. G. Hovanskii, Fewnomials and Pfaff manifolds, Proc. Ent. Congress of Mathematicians, Warsaw (1983) 549-564.
• [15] A. G. Hovanskii, Real analytic varieties with the finiteness property and complex abelian integrals. Punct. Anal. Appl., 18 (1984) 119-127.
• [16] A. G. Hovanskii, Fewnomials, Transl. Math. Monographs 88, Amer. Math. Soc., Providence 1991.
• [17] Yu. S. I`yashenko, Finiteness Theorems for Limit Cycles, Transh Math. Monographs 94, Amer. Math. Soc., Providence 1991.
• [18] M. Knebusch, Semialgebraic topology in the last ten years, in: Real Algebraic Geometry, Proceedings, Rennes 1991, Lect. Notes Math. 1524 1-36.
• [19] S. Łojasiewicz, Introduction to complex. Analytic Geometry, Birkhinser Verlag, 1991.
• [20] S. Łojasiewicz, Ensembles semianalytiques, I.II.E.S., Bures-sur-Yvette 1965.
• [21] S. Łojasiewicz, Sur l'adhércnce d'un ensemble partiellement semialgébrique, Publ. Math. LHES., 68 (1989) 205-210.
• [22] S. Łojasiewicz, M. A. Zurro, Introducción a la Geometría semi y sub-analítica, Universidad de Valladolid, 1993.
• [23] C. Miller, Expansions of the real field with power functions, Ann. Pure Appl. Logic, 68 (1994) 79-94.
• [24] R. Moussu, C. Roche, Probléme de Dulac et théorie dc Hovanskii, Invent. Math., 105 (1991) 431-441.
• [25] R. Moussu, C. Roche, Théorémes de finitude pour les variétés plaffiennes, Ann. Ins. Fourier Grenoble 42 (1-2) (1992) 393-420.
• [26] C. Roche, Densities for certain leaves of real analytic foliations, Astérisque, 222 (1994) 373-387.
• [27] A. Tarski, A Decision Method for Elementary Algebra and Geometry, 2nd ed., Berkeley and Los Angeles 1951.
• [28] Ta Lé Loi, On the global Łojasiewicz inequalities for the class of analytic logarithmico-exponential functions, C. R. Acad. Sci. Paris, 318, Série I (1994) 543-548.
• [29] R. Thom, Sur les bouts d'une feuille d'un feuilletage au voisinage d'un point singulier isolé, Proceedings Mexico 1986, Lect. Notes Math., Springer, 1345 317-321.
• [30] C. T. C. Wall, Regular stratifications, Proceedings Warwick 1974, beet. Notes Math., Springer, 468 332-314.
• [31] H. Whitney, Tangents to an Analytic Variety, Ann. Math., 81 (1965) 496-546.
• [32] A. J. Wilkie, Model completeness results for expansions of the ordered fiel of real numbers by restricted Pfaffian functions and the exponential function, J. Amer Math. Soc., 9 (1996) 1051-1094.