Parabolic resonances in 3 degree of freedom near-integrable Hamiltonian systems
UNSPECIFIED. (2002) Parabolic resonances in 3 degree of freedom near-integrable Hamiltonian systems. PHYSICA D-NONLINEAR PHENOMENA, 164 (3-4). pp. 213-250. ISSN 0167-2789Full text not available from this repository.
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
|Journal or Publication Title:||PHYSICA D-NONLINEAR PHENOMENA|
|Publisher:||ELSEVIER SCIENCE BV|
|Official Date:||15 April 2002|
|Number of Pages:||38|
|Page Range:||pp. 213-250|
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