CHAOTIC OSCILLATIONS OF A BUCKLED BEAM

Abstract

We show that the equation [Formula: see text], x ∈ (0, π), α < -1, which models transversal nonlinear vibrations of a buckled beam, has invariant four-dimensional manifolds of solutions containing periodic orbits with transversal homoclinic orbits to them. The basic tool used in the proof is a theorem concerning two degrees of freedom Hamiltonian systems with saddle-center loops.