The Fedoryuk Condition and the Łojasiewicz Exponent near a Fibre of a Polynomial
We give a description of the set of points for which the Fedoryuk condition fails in terms of the Łojasiewicz exponent at infinity near a fibre of a polynomial.
The Łojasiewicz gradient inequality in a neighbourhood of the fibre
Some estimates of the Łojasiewicz gradient exponent at infinity near any fibre of a polynomial in two variables are given. An important point in the proofs is a new Charzyński-Kozłowski-Smale estimate of critical values of a polynomial in one variable.
Two remarks on non-zero constant Jacobian polynomial maps of ℂ²
We present some estimates on the geometry of the exceptional value sets of non-zero constant Jacobian polynomial maps of ℂ² and their components.