A variational approach to chaotic dynamics in periodically forced nonlinear oscillators (Q1594905)

The authors prove that a class of problems containing the classical periodically forced pendulum equation displays the main features of chaotic dynamics. The approach is based on the construction of multi-bump type heteroclinic solutions to periodic orbits by the use of global variational methods. The use of the variational approach is often convenient because it does not require the system to be a small perturbation of a simpler one, needs in general only mild nondegeneracy conditions, and is powerful enough to detect the principal features of chaotic dynamics. The authors show that their results are in general valid for variational problems possessing two global minimizers, without assumptions on the space periodicity of the potential. On the other hand, the existence of consecutive minimizers is necessary in order to obtain multibump solutions.