Normal forms for high co-dimension bifurcations of nonlinear time-periodic systems with nonsemisimple eigenvalues (Q1866120)

From author's abstract: The normal forms are found for time-periodic nonlinear variational equations with arbitrary Jordan matrices undergoing perturbation of high codimension. The equations are transformed via the Lyapunov-Floquet transformation into an equivalent form in which the linear matrix is constant with degenerate eigenvalues. It is shown that time-dependent and time-independent nonlinear resonance terms remain in the normal form for various Jordan matrices; specifically, quadratic and cubic nonlinearity forms are calculated explicitly. A commutative system with cubic nonlinearities and a double inverted pendulum with a periodic follower force are used as illustrative examples.