On analytic equivalence of functions at infinity

✍ Scribed by Grzegorz Skalski

• Publisher: Elsevier Science
• Year: 2011
• Tongue: French
• Weight: 143 KB
• Volume: 135
• Category: Article
• ISSN: 0007-4497
• DOI: 10.1016/j.bulsci.2011.02.005

✦ Synopsis

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[x 1 , . . . , x n ] is greater or equal to k -1, then there exists ε > 0 such that for every polynomial P ∈ R[x 1 , . . . , x n ] 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.