Chaos in the beam equation
The authors prove existence of infinitely many periodic as well as aperiodic bounded solutions to a slowly periodically perturbed damped beam equation. Assuming that the reduced four dimensional ordinary differential equation has a homoclinic orbit the authors prove that its chaotic dynamics (Smale's horseshoe) can be embedded into the dynamics of the original damped beam equation.
periodically perturbed damped beam equation
scientific article; zbMATH DE number 2136643