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Abstrakty
A mapping F:Rn→Rm is called overdetermined if m>n. We prove that the calculations of both the local and global Łojasiewicz exponent of a real overdetermined polynomial mapping F:Rn→Rm can be reduced to the case m=n.
Słowa kluczowe
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Rocznik
Tom
Strony
27--34
Opis fizyczny
Bibliogr. 12 poz.
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autor
- Faculty of Mathematics and Computer Science University of Łódz Banacha 22 90-238 Łódz, Poland
autor
- Faculty of Mathematics and Computer Science University of Łódz Banacha 22 90-238 Łódz, Poland
Bibliografia
- [1] E. Cygan, A note on separation of algebraic sets and the Łojasiewicz exponent for polynomial mappings, Bull. Sci. Math. 129 (2005), 139–147.
- [2] E. Cygan, Intersection theory and separation exponent in complex analytic geometry, Ann. Polon. Math. 69 (1998), 287–299.
- [3] E. Cygan, T. Krasinski and P. Tworzewski, Separation of algebraic sets and the Łojasiewicz exponent of polynomial mappings, Invent. Math. 136 (1999), 75–87.
- [4] S. Łojasiewicz, Introduction to Complex Analytic Geometry, Birkhäuser, Basel, 1991.
- [5] A. Płoski, Sur l’exposant d’une application analytique. II, Bull. Polish Acad. Sci. Math. 33 (1985), 123–127.
- [6] T. Rodak and S. Spodzieja, Effective formulas for the Łojasiewicz exponent at infinity, J. Pure Appl. Algebra 213 (2009), 1816–1822.
- [7] T. Rodak and S. Spodzieja, Effective formulas for the local Łojasiewicz exponent, Math. Z. 268 (2011), 37–44.
- [8] T. Rodak and S. Spodzieja, Łojasiewicz exponent near the fibre of a mapping, Proc. Amer. Math. Soc. 139 (2011), 1201–1213.
- [9] S. Spodzieja, The Łojasiewicz exponent at infinity for overdetermined polynomial mappings, Ann. Polon. Math. 78 (2002), 1–10.
- [10] S. Spodzieja, Multiplicity and the Łojasiewicz exponent, Ann. Polon. Math. 73 (2000), 257–267
- [11] P. Tworzewski, Intersection theory in complex analytic geometry, Ann. Polon. Math. 62 (1995), 177–191.
- [12] H. Whitney, Tangents to an analytic variety, Ann. of Math. 81 (1965), 496–549.
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Bibliografia
Identyfikator YADDA
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