scholarly journals Łojasiewicz exponents of non-degenerate holomorohic and mixed functions

2018 ◽  
Vol 41 (3) ◽  
pp. 620-651 ◽  
Author(s):  
Mutsuo Oka
Keyword(s):  
Łojasiewicz Exponents

scholarly journals Algorithms for residues and Lojasiewicz exponents

2000 ◽  
Vol 153 (1) ◽  
pp. 27-44 ◽  
Author(s):  
M. Elkadi ◽  
B. Mourrain
Keyword(s):  
Łojasiewicz Exponents

scholarly journals Topological invariants of plane curve singularities: Polar quotients and Łojasiewicz gradient exponents

2019 ◽  
Vol 30 (14) ◽  
pp. 1950073 ◽  
Author(s):  
Hong-Duc Nguyen ◽  
Tien-Son Phạm ◽  
Phi-Dũng Hoàng
Keyword(s):  
Complex Plane ◽  
Plane Curve ◽  
Complex Variables ◽  
Topological Invariant ◽  
Topological Invariants ◽  
Real Plane ◽  
Plane Curve Singularities ◽  
Łojasiewicz Exponents ◽  
Curve Singularities ◽  
Formula Computing

In this paper, we study polar quotients and Łojasiewicz exponents of plane curve singularities, which are not necessarily reduced. We first show that, for complex plane curve singularities, the set of polar quotients is a topological invariant. We next prove that the Łojasiewicz gradient exponent can be computed in terms of the polar quotients, and so it is also a topological invariant. For real plane curve singularities, we also give a formula computing the Łojasiewicz gradient exponent via real polar branches. As an application, we give effective estimates of the Łojasiewicz exponents in the gradient and classical inequalities of polynomials in two (real or complex) variables.

scholarly journals Łojasiewicz exponents and singularities at infinity of polynomials in two complex variables

2005 ◽  
Vol 103 (1) ◽  
pp. 47-60 ◽  
Author(s):  
Janusz Gwoździewicz ◽  
Arkadiusz Płoski
Keyword(s):  
Complex Variables ◽  
Łojasiewicz Exponents

scholarly journals Mixed Łojasiewicz exponents and log canonical thresholds of ideals

2016 ◽  
Vol 220 (1) ◽  
pp. 223-245 ◽  
Author(s):  
Carles Bivià-Ausina ◽  
Toshizumi Fukui
Keyword(s):  
Log Canonical ◽  
Łojasiewicz Exponents

scholarly journals Newton-Puiseux approximation and Łojasiewicz exponents

2003 ◽  
Vol 26 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Hà Huy Vui ◽  
Phạm Tiến So'n
Keyword(s):  
Łojasiewicz Exponents
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