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Parabolic resonances in 3 degree of freedom near-integrable Hamiltonian systems
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UNSPECIFIED (2002) Parabolic resonances in 3 degree of freedom near-integrable Hamiltonian systems. PHYSICA D-NONLINEAR PHENOMENA, 164 (3-4). pp. 213-250. ISSN 0167-2789.
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Abstract
Perturbing an integrable 3 degree of freedom (d.o.f.) Hamiltonian system containing a normally parabolic 2-torus which is m-resonant (m = 1 or 2) creates a parabolic m-resonance (m-PR). PRs of different types are either persistent or of low co-dimension, hence they appear robustly in many applications. Energy-momenta bifurcation diagram is constructed as a tool for studying the global structure of 3 d.o.f. near-integrable systems. A link between the diagram shape, PR and the resonance structure is found. The differences between the dynamics appearing in 2 and 3 d.o.f. systems exhibiting PRs are studied analytically and numerically. The numerical study demonstrates that PRs are an unavoidable source of large and fast instabilities in typical 3 d.o.f. systems. (C) 2002 Elsevier Science B.V. All rights reserved.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Journal or Publication Title: | PHYSICA D-NONLINEAR PHENOMENA | ||||
| Publisher: | ELSEVIER SCIENCE BV | ||||
| ISSN: | 0167-2789 | ||||
| Official Date: | 15 April 2002 | ||||
| Dates: |
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| Volume: | 164 | ||||
| Number: | 3-4 | ||||
| Number of Pages: | 38 | ||||
| Page Range: | pp. 213-250 | ||||
| Publication Status: | Published |
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