A PATH CROSSING LEMMA AND APPLICATIONS TO NONLINEAR SECOND ORDER EQUATIONS UNDER SLOWLY VARYING PERTURBATIONS

@inproceedings{PASCOLETTI2011APC,
  title={A PATH CROSSING LEMMA AND APPLICATIONS TO NONLINEAR SECOND ORDER EQUATIONS UNDER SLOWLY VARYING PERTURBATIONS},
  author={ANNA PASCOLETTI and Fabio Zanolin},
  year={2011}
}
We present some recent results on the existence of periodic solutions and chaotic like dynamics for second order scalar nonlinear ODEs. The equations under consideration belong to a simple class of perturbed planar Hamiltonian systems with slowly varying periodic coefficients, a typical example being given by the pendulum equation with moving support. Although there is already a broad literature on this subject, our approach, based on the concept of stretching along the paths, appears new in… CONTINUE READING

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