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Licensed Unlicensed Requires Authentication Published by De Gruyter October 8, 2014

Bifurcation values and stability of algebras of bounded polynomials

Krzysztof Kurdyka, Maria Michalska and Stanisław Spodzieja
From the journal Advances in Geometry


We show a tight relation between bifurcation values of a fixed polynomial f ∈ R[X; Y] and the family of polynomials bounded on a set { x ∈ R2 | f(x) ≤ c}. If g ∈ R[X; Y] is bounded on {x ∈ R2 | f(x) ≤ c}, then it is bounded on the bigger set {x ∈ R2 | f(x) ≤ c̃} with c < c̃ provided that the interval [c; c̃] does not contain any complex bifurcation value at infinity of f.

Published Online: 2014-10-8
Published in Print: 2014-10-1

© 2014 by Walter de Gruyter Berlin/Boston

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