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Arnol'd V.I., Il'yashenko Yu.S. Ordinary differential equations // Encyclopaedia of Math. Sciences. Vol.1. 1988.
Hartman Ph. On local homeomorphisms of Euclidean Spaces // Bol.Soc. Mat. Mexicana. 1960. V.5. P.220–241.
Sternberg S. On the structure of local homeomorphisms of Euclidean n-space. II. // Amer. J. Math. 1958. V.80, No.3. P.623–631.
Chen K.T. Equivalence and decomposition of vector fields about an elementary critical point // Amer. J. Math. 1963. V.85, No.4. P.693–722.
Takens F. Partially hyperbolic fixed points // Topology. 1971. V.10, No.2. P.133–147.
Robinson R.C. Differentiable conjugacy near compact invariant manifolds // Bol. Soc. Brasil. Math. 1971. V.2, No.1. P.33–44.
Belitskii G.R. Normal forms, invariants and local mappings. Kiev, 1979 (in Russian).
Sell G.R. Smooth linearization near a fixed point // Amer. J. Math. 1985. V.107, No.5. P.1035–1091.
Samovol V.S. Linearization of systems of differential equations in the vicinity of invariant toroidal manifolds // Trudy Mosk. Mat. obshch. 1979. V.38. P.187–219 (in Russian).
Samovol V.S. Equivalence of systems of differential equations in the neighbourhood of a rest point // Trudy Mosk. Mat. obshch. 1982. V.44. P.213–234 (in Russian).
Samovol V.S. Linearization of an autonomous system in the neighbourhood of a hyperbolic rest point // Diff. uravn. 1987. V.23, No.6. P.1098–1099 (in Russian).
Samovol V.S. On smooth linearization of systems of differential equations in the neighbourhood of a saddle rest point // Uspekhi mat. nauk. 1988. T.43. No.4. P.223–224 (in Russian).
Samovol V.S. On some conditions sufficient for smooth linearlization of an autonomous system in the vicinity of a rest point // Izv.AN KazSSR. 1988, No.3. P.41–44 (in Russian).
Samovol V.S. Linearization of a system of ordinary differential equations in the neighbourhood of a rest point of the saddle type // DAN UkrSSR. Ser A. 1989. No.1. P.30–33 (in Russian).
Samovol V.S. On a necessary and sufficient condition for smooth linearization of an autonomous system on the plane in the vicinity of a rest point // Mat. Zametki. 1989. V.46, No.1. P.67–77 (in Russian).
Bronstein I.U., Kopanskii A.Ya. Finitely smooth polynomial normal forms of C∞-diffeomorphisms in the neighbourhood of a fixed point // Funk. analiz i ego prilozh. 1990. V.24, No.2. P.79–80. (in Russian).
Sternberg S. Local contractions and a theorem of Poincaré // Amer.J. Math. 1957. V.79, No.5. P.809–824.
Bronstein I.U., Kopanskii A.Ya. Invariant manifolds and normal forms. Kishinev. 1992 (in Russian).
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Bronstein, I.U., Kopanskii, A.Y. (1992). Finitely smooth normal forms of vector fields in the vicinity of a rest point. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis - Studies and Applications V. Lecture Notes in Mathematics, vol 1520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084720
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