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Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3

100%

Janczewska J., Maksymiuk J.

Open Mathematics

2012

tom 10

nr 6

1920-1927

We consider a conservative second order Hamiltonian system $$\ddot q + \nabla V(q) = 0$$ in ℝ3 with a potential V having a global maximum at the origin and a line l ∩ {0} = ϑ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.

The shadowing chain lemma for singular Hamiltonian systems involving strong forces

75%

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.

Ograniczanie wyników

2 Open Mathematics

2 Janczewska J.

1 Izydorek M.

1 Maksymiuk J.

2 2012

Wyniki wyszukiwania

Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3

The shadowing chain lemma for singular Hamiltonian systems involving strong forces