Abstract
We consider a planar autonomous Hamiltonian system :q+∇V(q) = 0, where the potential V: ℝ2 \{ζ}→ ℝ has a single well of infinite depth at some point ζ and a strict global maximum 0at two distinct points a and b. Under a strong force condition around the singularity ζ we will prove a lemma on the existence and multiplicity of heteroclinic and homoclinic orbits — the shadowing chain lemma — via minimization of action integrals and using simple geometrical arguments.
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Izydorek, M., Janczewska, J. The shadowing chain lemma for singular Hamiltonian systems involving strong forces. centr.eur.j.math. 10, 1928–1939 (2012). https://doi.org/10.2478/s11533-012-0107-6
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DOI: https://doi.org/10.2478/s11533-012-0107-6