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Periodically perturbed superlinear ODEs with singularities: subharmonic solutions and complex dynamics

Lakshmi Burra

IIIT di Hyderabad (India)

Abstract
We prove the existence of infinitely many subharmonic solutions as well as the presence of a full symbolic dynamics for a class of second-order nonlinear ordinary differential equations with a singularity of repulsive type at the origin and a superlinear growth at infinity. Our result, although dealing with a planar Hamiltonian system, is stable for small perturbations and we can allow the presence of a damping coefficient as well.