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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0107-6,
author = {Marek Izydorek and Joanna Janczewska},
title = {The shadowing chain lemma for singular Hamiltonian systems involving strong forces},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {1928-1939},
zbl = {1269.37015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0107-6}
}
Marek Izydorek; Joanna Janczewska. The shadowing chain lemma for singular Hamiltonian systems involving strong forces. Open Mathematics, Tome 10 (2012) pp. 1928-1939. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0107-6/
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