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3 Bulletin of the Polish Academy of Sciences. Mathematics

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The Fedoryuk condition and the Łojasiewicz exponent near a fibre of a polynomial

Rodak T.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 3

227-229

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.

On the Łojasiewicz exponent near the fibre of a polynomial

Skalski G.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 3

231-236

The equivalence of the definitions of the Łojasiewicz exponent introduced by Ha and by Chądzyński and Krasiński is proved. Moreover we show that if the above exponents are less than -1 then they are attained at a curve meromorphic at infinity.

On the Łojasiewicz exponent of the gradient of holomorphic functions

Bogusławska M.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 4

337-343

We show that the Łojasiewicz exponent L[sub o] (grad f) at zero of the gradient of a distinguished pseudo-polynomial f [...] is attained on the zero-set of f'[sub y].