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Instability with two zero frequencies. (English) Zbl 0792.34046

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.

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
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