Geodesic
Critical cases of stability. Converse implicit function theorem for dynamical systems with cosymmetry
Matematičeskie zametki, Tome 63 (1998) no. 4, pp. 572-578

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Stability criteria of boundary equilibria for dynamical systems in the three critical cases, $(n,k)=(3,0), (2,1)$, and $(1,1)$, are obtained. 
@article{MZM_1998_63_4_a9,
     author = {L. G. Kurakin},
     title = {Critical cases of stability. {Converse} implicit function theorem for dynamical systems with cosymmetry},
     journal = {Matemati\v{c}eskie zametki},
     pages = {572--578},
     publisher = {mathdoc},
     volume = {63},
     number = {4},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_4_a9/}
}
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L. G. Kurakin. Critical cases of stability. Converse implicit function theorem for dynamical systems with cosymmetry. Matematičeskie zametki, Tome 63 (1998) no. 4, pp. 572-578. http://geodesic.mathdoc.fr/item/MZM_1998_63_4_a9/