A Theorem on the Bifurcations of the Slow Invariant Manifold of a System of Two Linear Oscillators Coupled to a k-order Nonlinear Oscillator

摘要

we study a system of two linear oscillators coupled to a k-order non-linear oscillator with a mass much smaller than the mass of the linear oscillators. We prove that the Slow Invariant Manifold of the system may bifurcate only when the order of the nonlinear oscillator is an odd number.