Semi-invariant form of equilibrium stability criteria in critical cases. (English. Russian original) Zbl 0632.58028

J. Appl. Math. Mech. 50, 543-546 (1986); translation from Prikl. Mat. Mekh. 50, 707-711 (1986).
Expressions are given for the first coefficients of the normal form of the equations in the neutral equilibrium manifolds of an autonomous system in the basic critical cases, in terms of the neutral eigenvectors of the linearized system and its conjugate. Using the reduction principle [V. A. Pliss, Izv. Akad. Nauk SSSR, Ser. Mat. 28, 1297-1324 (1964; Zbl 0131.315)], the stability criteria previously obtained by various authors in critical cases take an explicit form, which is very convenient for calculations and does not involve the restriction of finite dimensionality.


37C10 Dynamics induced by flows and semiflows


Zbl 0131.315
Full Text: DOI


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