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INFINITE RELATIVE DETERMINACY OF SMOOTH FUNCTION GERMS WITH TRANSVERSE ISOLATED SINGULARITIES AND RELATIVE ŁOJASIEWICZ CONDITIONS

Published online by Cambridge University Press:  29 March 2004

V. GRANDJEAN
V. GRANDJEAN
Affiliation:
Department of Computer Science, University of Bath, Bath BA2 7AY, cssvg@bath.ac.uk
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Abstract

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.

Keywords

58C2758A2046E25 (primary)20G2057R45 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 518 - 530
Copyright
The London Mathematical Society 2004

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