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Infinitely Determined Mapgerms

Published online by Cambridge University Press:  20 November 2018

Leslie C. Wilson
Leslie C. Wilson*
Affiliation:
University of Hawaii, Honolulu, Hawaii
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In differential analysis, it is very useful to have the local behavior of a differentiable map be determined by the derivatives of the map at a point. Hence we have the theories of finite and infinitely determined germs. Let mnp be the space of germs of C∞ maps f: (Rn, 0) → (Rp, 0) and G a group operating on mnp. A germ f is called finitely G-determined if there exists an integer k such that every germ having the same k-jet as f is G-equivalent to (i.e., in the same G-orbit as) f. A germ f is called ∞-G-determined if every germ having the same formal power series as f is G-equivalent to f.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 3 , 01 June 1981 , pp. 671 - 684
Copyright
Copyright © Canadian Mathematical Society 1981

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