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
Journal or Publication Title:	PHYSICA D-NONLINEAR PHENOMENA
Publisher:	ELSEVIER SCIENCE BV
ISSN:	0167-2789
Official Date:	15 April 2002
Dates:	Date Event 15 April 2002 UNSPECIFIED
Volume:	164
Number:	3-4
Number of Pages:	38
Page Range:	pp. 213-250
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/10869

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