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Infinite Relative Determinacy of Smooth Function Germs with Transverse Isolated Singularities and Relative Łojasiewicz Conditions
Author(s) -
Grandjean V.
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703004861
Subject(s) - gravitational singularity , determinacy , mathematics , function (biology) , transverse plane , mathematical analysis , pure mathematics , engineering , structural engineering , biology , evolutionary biology
Sun and Wilson defined the notion of infinite determinacy of a smooth function germ singular along a line, and related this notion to some good geometric properties of derived objects related to the given function germ. The paper extends their results to a wider class of smooth function with prescribed non‐isolated singularities. For this purpose, it was necessary to study the behaviour of the function germ along a transverse direction of the given singular set, and to relate these properties to geometric properties of the function and derived objects, expressed in terms of relative Łojasiewicz conditions.