On analytic equivalence of functions at infinity

摘要

In this paper we define the relation of analytic equivalence of functions at infinity. We prove that if the Lojasiewicz exponent at infinity of the gradient of a polynomial f is an element of R[x(1) ,..., x(n)] is greater or equal to k - 1, then there exists epsilon > 0 such that for every polynomial P is an element of R[x(1) ,..., x(n)] of degree less or equal to k, whose coefficients of monomials of degree k are less or equal epsilon, the polynomials f and f + P are analytically equivalent at infinity.