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The shadowing chain lemma for singular Hamiltonian systems involving strong forces

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Izydorek M., Janczewska J.

Open Mathematics

2012

tom 10

nr 6

1928-1939

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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1 Open Mathematics

1 Izydorek M.

1 Janczewska J.

1 2012

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The shadowing chain lemma for singular Hamiltonian systems involving strong forces