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Dual pairs in resonances
1. | Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom |
2. | Department of Mathematics, West University of Timişoara, 300223 Timişoara, Romania |
References:
[1] |
R. Cushman and D. L. Rod, Reduction of the semisimple $1:1$ resonance,, Physica D, 6 (1982), 105.
|
[2] |
A. Elipe, Complete reduction of oscillators in resonance $p:q$,, Phys. Rev. E, 61 (2000), 6477. Google Scholar |
[3] |
F. Fassò, Superintegrable Hamiltonian systems: Geometry and perturbations,, Acta Appl. Math., 87 (2005), 93.
|
[4] |
F. Gay-Balmaz and C. Vizman, Dual pairs in fluid dynamics,, Ann. Global. Anal. Geom., ().
|
[5] |
D. D. Holm, "Geometric Mechanics Part 1: Dynamics and Symmetry,", World Scientific, (2008).
|
[6] |
D. D. Holm and J. E. Marsden [2004], Momentum maps and measure-valued solutions (peakons, filaments and sheets) for the EPDiff equation, in The Breadth of Symplectic and Poisson Geometry,, A Festshrift for Alan Weinstein, 232 (2004), 203. Google Scholar |
[7] |
T. Iwai, On reduction of two degrees of freedom Hamiltonian systems by an $S^1$ action and $SO_0(1,2)$ as a dynamical group,, J. Math. Phys., 26 (1985), 885.
|
[8] |
M. Kummer, On resonant nonlinearly coupled oscillators with two equal frequencies,, Commun. Math. Phys., 48 (1976), 53.
|
[9] |
M. Kummer, On resonant classical Hamiltonians with two equal frequencies,, Commun. Math. Phys., 58 (1978), 85.
doi: 10.1007/BF01624789. |
[10] |
M. Kummer, On the construction of the reduced phase space of a Hamiltonian system with symmetry,, Indiana Univ. Math. J., 30 (1981), 281.
doi: 10.1512/iumj.1981.30.30022. |
[11] |
M. Kummer, On resonant Hamiltonian systems with finitely many degrees of freedom,, in, 252 (1986), 19.
|
[12] |
J. E. Marsden, Generic Bifurcation of Hamiltonian Systems with Symmetry, appendix to Golubitsky and Stewart, Physica D,, 24 (1987), 24 (1987), 391.
|
[13] |
J. E. Marsden and A. Weinstein, Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids,, Phys. D, 7 (1983), 305. Google Scholar |
[14] |
A. S. Mishenko and A. T. Fomenko, Generalized Liouville method of integration of Hamiltonian systems,, Funct. Anal. Appl., 12 (1978), 113. Google Scholar |
[15] |
J.-P. Ortega and T. S. Ratiu, "Momentum Maps and Hamiltonian Reduction,", Progress in Mathematics (Boston, 222 (2004).
|
[16] |
A. Weinstein, The local structure of Poisson manifolds,, J. Diff. Geom., 18 (1983), 523.
|
show all references
References:
[1] |
R. Cushman and D. L. Rod, Reduction of the semisimple $1:1$ resonance,, Physica D, 6 (1982), 105.
|
[2] |
A. Elipe, Complete reduction of oscillators in resonance $p:q$,, Phys. Rev. E, 61 (2000), 6477. Google Scholar |
[3] |
F. Fassò, Superintegrable Hamiltonian systems: Geometry and perturbations,, Acta Appl. Math., 87 (2005), 93.
|
[4] |
F. Gay-Balmaz and C. Vizman, Dual pairs in fluid dynamics,, Ann. Global. Anal. Geom., ().
|
[5] |
D. D. Holm, "Geometric Mechanics Part 1: Dynamics and Symmetry,", World Scientific, (2008).
|
[6] |
D. D. Holm and J. E. Marsden [2004], Momentum maps and measure-valued solutions (peakons, filaments and sheets) for the EPDiff equation, in The Breadth of Symplectic and Poisson Geometry,, A Festshrift for Alan Weinstein, 232 (2004), 203. Google Scholar |
[7] |
T. Iwai, On reduction of two degrees of freedom Hamiltonian systems by an $S^1$ action and $SO_0(1,2)$ as a dynamical group,, J. Math. Phys., 26 (1985), 885.
|
[8] |
M. Kummer, On resonant nonlinearly coupled oscillators with two equal frequencies,, Commun. Math. Phys., 48 (1976), 53.
|
[9] |
M. Kummer, On resonant classical Hamiltonians with two equal frequencies,, Commun. Math. Phys., 58 (1978), 85.
doi: 10.1007/BF01624789. |
[10] |
M. Kummer, On the construction of the reduced phase space of a Hamiltonian system with symmetry,, Indiana Univ. Math. J., 30 (1981), 281.
doi: 10.1512/iumj.1981.30.30022. |
[11] |
M. Kummer, On resonant Hamiltonian systems with finitely many degrees of freedom,, in, 252 (1986), 19.
|
[12] |
J. E. Marsden, Generic Bifurcation of Hamiltonian Systems with Symmetry, appendix to Golubitsky and Stewart, Physica D,, 24 (1987), 24 (1987), 391.
|
[13] |
J. E. Marsden and A. Weinstein, Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids,, Phys. D, 7 (1983), 305. Google Scholar |
[14] |
A. S. Mishenko and A. T. Fomenko, Generalized Liouville method of integration of Hamiltonian systems,, Funct. Anal. Appl., 12 (1978), 113. Google Scholar |
[15] |
J.-P. Ortega and T. S. Ratiu, "Momentum Maps and Hamiltonian Reduction,", Progress in Mathematics (Boston, 222 (2004).
|
[16] |
A. Weinstein, The local structure of Poisson manifolds,, J. Diff. Geom., 18 (1983), 523.
|
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