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On the support of solutions to the Kadomtsev-Petviashvili (KP-II) equation
On the similarity of Hamiltonian and reversible vector fields in 4D
1. | Department of Mathematics, IMECC, Unicamp, 13083-970, Campinas SP, Brazil |
2. | Departamento de Matemática, Universidade Estadual de Campinas, Caixa Postal 6065, 13083-970, Campinas, S.P., Brazil |
References:
[1] |
R. Abraham and J. Marsden, "Foundations of Mechanics," Benjamin Cummings, London, 1978. |
[2] |
V. I. Arnold, "Arnold's Problems," Springer-Verlag, Berlin, 2004. |
[3] |
V. I. Arnold, "Geometrical Methods in the Theory of Ordinary Differential Equations,'' Springer-Verlag, New York, 1988. |
[4] |
G. D. Birkhoff, Dynamical systems with two degrees of freedom, Trans. Amer. Math. Soc., 18 (1917), 199-300.
doi: 10.2307/1988861. |
[5] |
R. L. Devaney, Reversible diffeomorphisms and flows, Trans. Amer. Math. Soc., 218 (1976), 89-113.
doi: 10.2307/1997429. |
[6] |
G. Gaeta, Normal Forms of reversible dynamical systems, International Journal of Theoretical Physics, 33 (1994), 1917-1928.
doi: 10.1007/BF00671033. |
[7] |
A. Jacquemard, M. F. S. Lima and M. A. Teixeira, Degenerate resonances and branching of periodic orbits, Annali di Matematica Pura ed Applicata, 187 (2008), 105-117. |
[8] |
J. S. W. Lamb, M. F. S. Lima, R. M. Martins, M. A. Teixeira and J. Yang, On the Hamiltonian structure of normal forms at elliptic equilibria of reversible vector fields in $R^4$, IMECC/Unicamp Research Report 05/10, 2010. Available from: http://www1.ime.unicamp.br/rel_pesq/relatorio.html. |
[9] |
J. C. van der Meer, J. A. Sanders and A. Vanderbauwhede, Hamiltonian Structure of the Reversible Nonsemisimple $1:1$ Resonance, in "Dynamics, Bifurcation and Symmetry: New Trends and New Tools", Kluwer Academic Publishers, (1994), 221-240. |
[10] |
G. B. Price, On reversible dynamical systems, Trans. Amer. Math. Soc., 37 (1935), 51-79.
doi: 10.2307/1989695. |
[11] |
M. A. Teixeira, Singularities of reversible vector fields, Phys. D, 100 (1997), 101-118.
doi: 10.1016/S0167-2789(96)00183-2. |
show all references
References:
[1] |
R. Abraham and J. Marsden, "Foundations of Mechanics," Benjamin Cummings, London, 1978. |
[2] |
V. I. Arnold, "Arnold's Problems," Springer-Verlag, Berlin, 2004. |
[3] |
V. I. Arnold, "Geometrical Methods in the Theory of Ordinary Differential Equations,'' Springer-Verlag, New York, 1988. |
[4] |
G. D. Birkhoff, Dynamical systems with two degrees of freedom, Trans. Amer. Math. Soc., 18 (1917), 199-300.
doi: 10.2307/1988861. |
[5] |
R. L. Devaney, Reversible diffeomorphisms and flows, Trans. Amer. Math. Soc., 218 (1976), 89-113.
doi: 10.2307/1997429. |
[6] |
G. Gaeta, Normal Forms of reversible dynamical systems, International Journal of Theoretical Physics, 33 (1994), 1917-1928.
doi: 10.1007/BF00671033. |
[7] |
A. Jacquemard, M. F. S. Lima and M. A. Teixeira, Degenerate resonances and branching of periodic orbits, Annali di Matematica Pura ed Applicata, 187 (2008), 105-117. |
[8] |
J. S. W. Lamb, M. F. S. Lima, R. M. Martins, M. A. Teixeira and J. Yang, On the Hamiltonian structure of normal forms at elliptic equilibria of reversible vector fields in $R^4$, IMECC/Unicamp Research Report 05/10, 2010. Available from: http://www1.ime.unicamp.br/rel_pesq/relatorio.html. |
[9] |
J. C. van der Meer, J. A. Sanders and A. Vanderbauwhede, Hamiltonian Structure of the Reversible Nonsemisimple $1:1$ Resonance, in "Dynamics, Bifurcation and Symmetry: New Trends and New Tools", Kluwer Academic Publishers, (1994), 221-240. |
[10] |
G. B. Price, On reversible dynamical systems, Trans. Amer. Math. Soc., 37 (1935), 51-79.
doi: 10.2307/1989695. |
[11] |
M. A. Teixeira, Singularities of reversible vector fields, Phys. D, 100 (1997), 101-118.
doi: 10.1016/S0167-2789(96)00183-2. |
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