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Journal of the London Mathematical Society (1)

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INFINITE RELATIVE DETERMINACY OF SMOOTH FUNCTION GERMS WITH TRANSVERSE ISOLATED SINGULARITIES AND RELATIVE ŁOJASIEWICZ CONDITIONS
V. GRANDJEAN
Journal:

Journal of the London Mathematical Society / Volume 69 / Issue 2 / April 2004

Published online by Cambridge University Press:

29 March 2004, pp. 518-530

Print publication:

April 2004
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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.