H W Broer et al 1998 Nonlinearity 11 1569 doi:10.1088/0951-7715/11/6/009
Resonances in a spring-pendulum: algorithms for equivariant singularity theory
H W Broer, I Hoveijn, G A Lunter and G Vegter
Show affiliationsRecommended by J Laska
A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained. The reduction is handled by equivariant singularity theory with a distinguished parameter, yielding an integrable approximation of the Poincaré map. This makes a concise description of certain bifurcations possible. The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.
- PACS
- MSC
-
37D50 Hyperbolic systems with singularities (billiards, etc.)
70H08 Nearly integrable Hamiltonian systems, KAM theory
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws
- Subjects
- Dates
-
Issue 6 (November 1998)
Received 11 November 1997, in final form 22 July 1998
-
Resonances in a spring-pendulum: algorithms for equivariant singularity theory
H W Broer et al 1998 Nonlinearity 11 1569
-
Bifurcations and strange attractors in the Lorenz-84 climate model with seasonal forcing
Henk Broer et al 2002 Nonlinearity 15 1205
-
Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach
Henk Broer et al 2003 Nonlinearity 16 1751
-
The geometry of resonance tongues: a singularity theory approach
Henk W Broer et al 2003 Nonlinearity 16 1511
-
Towards global models near homoclinic tangencies of dissipative diffeomorphisms
Henk Broer et al 1998 Nonlinearity 11 667
-
Nanotechnology, resources, and pollution control
Stephen L Gillett 1996 Nanotechnology 7 177
-
Diffraction by a grating made of a uniaxial dielectric–magnetic medium exhibiting negative refraction
Ricardo A Depine and Akhlesh Lakhtakia 2005 New J. Phys. 7 158
-
Negative phase velocity in a material with simultaneous mirror-conjugated and racemic chirality characteristics
Tom G Mackay and Akhlesh Lakhtakia 2005 New J. Phys. 7 165
-
Laser-driven photo-transmutation of 129I—a long-lived nuclear waste product
K W D Ledingham et al 2003 J. Phys. D: Appl. Phys. 36 L79
-
Multithreading for synchronization tolerance in matrix factorization
Alfredo Buttari et al 2007 J. Phys.: Conf. Ser. 78 012028
Related review articles
What's this?- Dimension of non-conformal repellers: a survey
- Progress in normal form theory
- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
, and Chern–Simons–Higgs solitons on 
: dimensional reduction of Chern–Pontryagin densities