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Some Łojasiewicz inequalities at infinity for the gradient of a polynomial are given.
Wydawca
Rocznik
Tom
Strony
273--281
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
- Faculty of Mathematics, University of Łódź, S. Banacha 22, 90-238 Łódź, Poland
Bibliografia
- [1] J. Bochnak. S. Łojasiewicz, A converse of the Kuiper-Kuo theorem, Proc. of Liverpool Singularities-Symposium I, Liverpool (1969/1970) 254-261, Lecture Notes in Math., 192, Springer, Berlin (1971) 254-261.
- [2] J. Chądzyński, T. Krasiński, A set on which the Łojasiewicz exponent at infinity is attained, Ann. Polon. Math., 67 (1997) 191-197.
- [3] J. Chądzyński, T. Krasiński, Exponent of growth of polynomial mappings of C2 into C2, in: Singularities, Banach Center Publications, 20, PWN, Warszawa (1988) 147-160.
- [4] J. Chądzyński, T. Krasiński, On the Łojasiewicz exponent at infinity for polynomial mapping of C2 into C2 and components of polynomial automorphisms of C2, Ann. Polon. Math., 57 (1992) 291-302.
- [5] A. H. Durfee, Five definitions of critical points at infinity, in: Singularities (Oberwolfach 1996), Progr. Math., 162, Birkhäuser, Basel (1998) 345-360.
- [6] M. V. Fedorjuk, The asymptotic of the Fourier tranform of the exponential function of a polynomial (in Russian), Dokl. Akad. Nauk. SSSR, 227 (1976) 580-583; English transl. in: Soviet Math. Dokl., 17 (2) (1976) 486-490.
- [7] H. V. Ha, Nombres de Łojasiewicz et singularités à l’infini des polynômes de deux variables complexes, C. R. Acad. Sci. Paris Sér. I Math., 311 (1990) 429-432.
- [8] L. Hörmander, On the division of distribution by polynomials, Ark. Mat., 3 (1958) 555-568.
- [9] Z. Jelonek, The set of points at which a polynomial map is not proper, Ann. Polon. Math., 58 (1993) 259-266.
- [10] Z. Jelonek, K. Kurdyka, On asymptotic critical values of a complex polynomial, preprint IMPAN, Warszawa 2001.
- [11] T. Krasiński, The level sets of polynomials in two variables and jacobian hypothesis (in Polish), University of Łódź Press, Łódź 1991.
- [12] T. C. Kuo, A. Parusiński, Newton polygon relative to an arc, in: Real and Complex Singularities (São Carlos 1998), CRC Res. Notes Math., 412 (2000) 76-93.
- [13] K. Kurdyka, T. Mostowski, A. Parusiński, Proof of the gradient conjecture of R. Thom, Ann. of Math., 152 (2000) 763-792.
- [14] S. Łojasiewicz, Ensembles semi-analytiques, Publ. Math, IHES, Bues-sur-Yvette, 1965.
- [15] S. Łojasiewicz, Introduction to complex analytic geometry, Birkhäuser, Basel Boston Berlin 1991.
- [16] D. Mumford, Algebraic geometry I; Complex projective varieties, Springer, Berlin Heidelberg New York 1976.
- [17] A. Némethi, A. Zaharia, Milnor fibration at infinity, Indag. Math., 3 (1992) 323-335.
- [18] A. Parusiński, On the bifurcation set of complex polynomial with isolated singularities at infinity, Compositio Math., 97 (1995) 369-384.
- [19] L. Păunescu, A. Zaharia, On the Łojasiewicz exponent at infinity for polynomial functions, Kodai Math. J., 20 (1997) 269-274.
- [20] F. Pham, La descente des cols par les onglets de Lefschetz, avec vues sur Gauss-Manin, in: Systèmes différentiels et singularitiés, (Luminy 1983), Astérisque, 130 (1985) 11-47.
- [21] A. Płoski, An inequality for polynomial mappings, Bull. Pol. Ac.: Math., 40 (1992) 265-269.
- [22] A. Płoski, P. Tworzewski, A separation condition for polynomial mappings, Bull. Pol. Ac.: Math., 44 (1996) 327-331.
- [23] P. J. Rabier, Ehresmann’s fibrations and Palais-Smale conditions for morphismes of Finsler manifolds, Ann. of Math., 146 (1997) 647-691.
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Bibliografia
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bwmeta1.element.baztech-article-BAT2-0001-0842