Characterization of v-sufficiency from the Newton filtration

The newton filtration and d-determination of bifurcation problems related to C 0 contact equivalence

“…Thus we can choose a small neighborhood V of 0 such that V ⊂ W, define ψ : V ×I → W ×I such that (u, t) → ψ(u, t) is a integral curve satisfying ψ(u, 0) = u. By the theory of local flow we know ψ is a homeomorphism from V × I to ψ(V × I) and by (8) we have ψ(u, t) = (ψ 1 (u, t), t).…”

“…Percell and Brown [5] , Sun [6] and Zou [7] generalized C ∞ contact equivalence to C 0 contact equivalence in studying bifurcation problems. In 2005, Abdewahamane [8] introduced the sigular Riemannian metric adapted to the Newton polyhedron Γ and he defined the gradient of f with respect to Γ, then he gave the characterization of V -sufficiency. Using this construction, we have obtained the version of bifurcation problem related to the Newton filtration.…”