On the Łojasiewicz exponent of the gradient of a holomorphic function

Volume 44 / 1998

Andrzej Lenarcik Banach Center Publications 44 (1998), 149-166 DOI: 10.4064/-44-1-149-166


The Łojasiewicz exponent of the gradient of a convergent power series h(X,Y) with complex coefficients is the greatest lower bound of the set of λ > 0 such that the inequality $|grad h(x,y)| ≥ c|(x,y)|^λ$ holds near $0 ∈ C^2$ for a certain c > 0. In the paper, we give an estimate of the Łojasiewicz exponent of grad h using information from the Newton diagram of h. We obtain the exact value of the exponent for non-degenerate series.


  • Andrzej Lenarcik

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