Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
Let F = X + H be a cubic homogeneous polynomial automorphism from $ℂ^n$ to $ℂ^n$. Let $p$ be the nilpotence index of the Jacobian matrix JH. It was conjectured by Drużkowski and Rusek in [4] that $deg F^{-1} ≤ 3^{p-1}$. We show that the conjecture is true if n ≤ 4 and false if n ≥ 5.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
173-176
Opis fizyczny
Daty
wydano
1995
otrzymano
1995-02-01
Twórcy
autor
- Department of Mathematics, University of Nijmegen, Nijmegen, The Netherlands
Bibliografia
- [1] H. Bass, E. Connell, and D. Wright, The Jacobian Conjecture: reduction of degree and formal expansion of the inverse, Bull. Amer. Math. Soc. 7 (1982), 287-330.
- [2] L. M. Drużkowski, An effective approach to Keller's Jacobian Conjecture, Math. Ann. 264 (1983), 303-313.
- [3] L. M. Drużkowski, The Jacobian Conjecture: some steps towards solution, in: Automorphisms of Affine Spaces, Proc. Conf. 'Invertible Polynomial Maps', Curaçao, July 4-8, 1994, A. R. P. van den Essen (ed.), Caribbean Mathematics Foundation, Kluwer Academic Publishers, 1995, 41-54.
- [4] L. M. Drużkowski and K. Rusek, The formal inverse and the Jacobian conjecture, Ann. Polon. Math. 46 (1985), 85-90.
- [5] E.-M. G. M. Hubbers, The Jacobian Conjecture: cubic homogeneous maps in dimension four, master thesis, Univ. of Nijmegen, February 17, 1994; directed by A. R. P. van den Essen.
- [6] K. Rusek and T. Winiarski, Polynomial automorphisms of $C^n$, Univ. Iagel. Acta Math. 24 (1984), 143-149.
- [7] A. V. Yagzhev, On Keller's problem, Siberian Math. J. 21 (1980), 747-754.
- [8] J.-T. Yu, On the Jacobian Conjecture: reduction of coefficients, J. Algebra 171 (1995), 515-523.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv62z2p173bwm