收稿日期: 2012-06-07
修回日期: 2012-08-31
网络出版日期: 2013-07-15
基金资助
Supported by the National Natural Science Foundation of China (11071247)
Polynomial automorphisms and Jacobian conjecture in two variables
Received date: 2012-06-07
Revised date: 2012-08-31
Online published: 2013-07-15
严丹 , 唐国平 . 二维的雅克比猜想和自同构多项式[J]. 中国科学院大学学报, 2013 , 30(4) : 438 -442 . DOI: 10.7523/j.issn.2095-6134.2013.04.002
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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