On stability and the Łojasiewicz exponent at infinity of coercive polynomials

Tomás Bajbar, Sönke Behrends

Abstract: In this article we analyze the relationship between the growth and stability properties of coercive polynomials. For coercive polynomials we introduce the degree of stable coercivity which measures how stable the coercivity is with respect to small perturbations by other polynomials. We link the degree of stable coercivity to the Łojasiewicz exponent at infinity and we show an explicit relation between them.