Follow the link on the author's name for a listing of that particular author's tech reports, or follow the link in Keywords or Thrust area for a listing of tech reports with similar keywords. Abstract Liapunov functions are constructed for nonlinear systems of ordinary differential equations whose linearized system at an equilibrium point possesses either a simple zero eigenvalue or a complex conjugate pair of simple, pure emaginary eigenvalues. The construction is explicit, and yields parametrized families of Liapunov functions for such systems. In the case of a zero eigenvalue, the Liapunov functions contain quadratic and cubic terms in the state.
Quadratic terms appear as well for the case of a pair of pure imaginary eigenvalues.
Predictions of local asymptotic stability using these Liapunov functions are shown to coincide with those of pertinent bifurcation-theoretic calculations. The development of the paper is carried out using elementary properties of multilinear functions. The Liapunov function families thus obtained are amendable to symbolic computer coding.