Geodesic
Infinitely Determined Mapgerms
Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 671-684

Voir la notice de l'article provenant de la source Cambridge University Press

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: (R n , 0) → (R p , 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. 
Wilson, Leslie C. Infinitely Determined Mapgerms. Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 671-684. doi: 10.4153/CJM-1981-053-3
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