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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

1 Issue per year


IMPACT FACTOR 2016 (Open Mathematics): 0.682
IMPACT FACTOR 2016 (Central European Journal of Mathematics): 0.489

CiteScore 2016: 0.62

SCImago Journal Rank (SJR) 2016: 0.454
Source Normalized Impact per Paper (SNIP) 2016: 0.850

Mathematical Citation Quotient (MCQ) 2016: 0.23

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ISSN
2391-5455
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Volume 10, Issue 6 (Dec 2012)

Issues

The shadowing chain lemma for singular Hamiltonian systems involving strong forces

Marek Izydorek
  • Faculty of Technical Physics and Applied Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-233, Gdańsk, Poland
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/ Joanna Janczewska
  • Faculty of Technical Physics and Applied Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-233, Gdańsk, Poland
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Published Online: 2012-10-12 | DOI: https://doi.org/10.2478/s11533-012-0107-6

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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About the article

Published Online: 2012-10-12

Published in Print: 2012-12-01


Citation Information: Open Mathematics, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-012-0107-6.

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

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