Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4669015 | Bulletin des Sciences Mathématiques | 2011 | 14 Pages |
Abstract
In this paper we define the relation of analytic equivalence of functions at infinity. We prove that if the Łojasiewicz exponent at infinity of the gradient of a polynomial f∈R[x1,…,xn] is greater or equal to k−1, then there exists ε>0 such that for every polynomial P∈R[x1,…,xn] of degree less or equal to k, whose coefficients of monomials of degree k are less or equal ε, the polynomials f and f+P are analytically equivalent at infinity.
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Physical Sciences and Engineering
Mathematics
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