Finite Determinacy of High Codimension Smooth Function Germs

(整期优先)网络出版时间:2019-01-11
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Mathergavethenecessaryandsufficientconditionsforthefinitedeterminacys-moothfunctiongermswithnomorethancodimension4.Thetheoremisveryeffectiveondetermininglowcodimensionsmoothfunctiongerms.Inthispaper,theconceptofrightequivalentforsmoothfunctiongermsringgeneratedbytwoidealsfinitelyisdefined.Thecontainmentrelationshipsoffunctiongermsstillsatisfyfinitek-determinacyundersufficientlysmalldisturbancewhicharediscussedinorbittangentspaces.Furthermore,themethodsinjudgingtherightequivalencyofArnoldfunctionfamilywithcodimension5arepresented.