The Łojasiewicz gradient inequality in a neighbourhood of the fibre

Volume 87 / 2005

Janusz Gwoździewicz, Stanisław Spodzieja Annales Polonici Mathematici 87 (2005), 151-163 MSC: 14E05, 14R25, 30C15. DOI: 10.4064/ap87-0-12


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 Charzy/nski–Kozłowski–Smale estimate of critical values of a polynomial in one variable.


  • Janusz GwoździewiczDepartment of Mathematics
    Technical University
    Al. Tysiąclecia Państwa Polskiego 7
    25-314 Kielce, Poland
  • Stanisław SpodziejaFaculty of Mathematics
    University of Łódź
    Banacha 22
    90-238 Łódź, Poland

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