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中国科学院大学学报 ›› 2013, Vol. 30 ›› Issue (4): 438-442.DOI: 10.7523/j.issn.2095-6134.2013.04.002

• 数学 • 上一篇    下一篇

二维的雅克比猜想和自同构多项式

严丹, 唐国平   

  1. 中国科学院大学数学学院, 北京 100049
  • 收稿日期:2012-06-07 修回日期:2012-08-31 发布日期:2013-07-15
  • 通讯作者: 严丹
  • 基金资助:

    Supported by the National Natural Science Foundation of China (11071247) 

Polynomial automorphisms and Jacobian conjecture in two variables

YAN Dan, TANG Guo-Ping   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2012-06-07 Revised:2012-08-31 Published:2013-07-15

摘要:

首先给出二维自同构多项式的求逆公式,如果有1个多项式的次数为素数;其次,证明二维自同构多项式是线性可上三角化,如果2个多项式的次数都为素数;最后,给出一种方法找到二维自同构多项式的逆,而且可以很快找到它们的逆,如果给定nm,其中n为多项式F1的次数,nm为多项式F2的次数.

关键词: 雅克比猜想, 多项式映射, 求逆公式

Abstract:

In this paper, we first give the inverse formula of polynomial automorphisms in two variables if one of the polynomials' degrees is prime. Secondly, we prove that the polynomial automorphisms in two variables are linearly triangularizable if the polynomials' degrees are primes. Finally, we give a way to find the inverse of the polynomial automorphisms in two variables in other cases and give the exact form of their inverses if n and m are fixed, where n=degF1 and nm=degF2.

Key words: Jacobian conjecture, polynomial mapping, inverse formula

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