二维的雅克比猜想和自同构多项式(英文)

Polynomial automorphisms and Jacobian conjecture in two variables

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n和m,其中n为多项式F1的次数,nm为多项式F2的次数.

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 = degF 1 and nm = degF 2.