Instability with two zero frequencies. (English) Zbl 0792.34046

Wiener, Z.

J. Differ. Equations 103, No. 1, 58-67 (1993).

The instability of a degenerate equilibrium position is studied through the formal solutions. The inversion of the Lagrange-Dirichlet stability theorem is proved in the case of two zero eigenvalues and a nondegenerate Newton’s diagram. This case includes all singularities appearing in a nonremovable way in families depending on not more than 16 parameters.

Reviewer: L.M.Perko (Flagstaff)

MSC:

34D05	Asymptotic properties of solutions to ordinary differential equations
34A25	Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34A09	Implicit ordinary differential equations, differential-algebraic equations
37C75	Stability theory for smooth dynamical systems
34C05	Topological structure of integral curves, singular points, limit cycles of ordinary differential equations

Keywords:

instability of a degenerate equilibrium position; formal solutions; inversion of the Lagrange-Dirichlet stability theorem; nondegenerate Newton’s diagram