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Open Mathematics

formerly Central European Journal of Mathematics


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The shadowing chain lemma for singular Hamiltonian systems involving strong forces

1Faculty of Technical Physics and Applied Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-233, Gdańsk, Poland

© 2012 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citation Information: Open Mathematics. Volume 10, Issue 6, Pages 1928–1939, ISSN (Online) 2391-5455, DOI: 10.2478/s11533-012-0107-6, October 2012

Publication History

Published Online:
2012-10-12

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.

MSC: 58F05; 34C37; 70H05

Keywords: Heteroclinic orbit; Homoclinic orbit; Rotation number (winding number); Shadowing chain lemma; Singular Hamiltonian systems; Strong force

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