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Formal equivalence between normal forms of reversible and hamiltonian dynamical systems
1. | Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, 13083–859 Campinas, SP |
References:
[1] |
R. Abraham and J. Marsden, "Foundations of Mechanics,", Benjamin Cummings, (1978).
|
[2] |
F. Antoneli, P. H. Baptistelli, A. P. Dias and M. Manoel, Invariant theory and reversible-equivariant vector fields,, J. Pure Appl. Algebra, 213 (2009), 649.
doi: 10.1016/j.jpaa.2008.08.002. |
[3] |
V. I. Arnold, "Arnold's Problems,", Springer-Verlag, (2004).
|
[4] |
V. I. Arnold, "Geometrical Methods in the Theory of Ordinary Differential Equations,", Fundamental Principles of Mathematical Sciences {\bf 250}. Springer-Verlag, 250 (1998).
|
[5] |
G. D. Birkhoff, Dynamical systems with two degrees of freedom,, Trans. Amer. Math. Soc., 18 (1917), 199.
doi: 10.1090/S0002-9947-1917-1501070-3. |
[6] |
R. L. Devaney, Reversible diffeomorphisms and flows,, Trans. Amer. Math. Soc., 218 (1976), 89.
doi: 10.1090/S0002-9947-1976-0402815-3. |
[7] |
G. Gaeta, Normal forms of reversible dynamical systems,, International Journal of Theoretical Physics, 33 (1994), 1917.
doi: 10.1007/BF00671033. |
[8] |
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.
doi: 10.1007/s10231-006-0036-8. |
[9] |
R. M. Martins and M. A. Teixeira, On the Similarity of Hamiltonian and reversible vector fields in 4D,, Communications on Pure and Applied Analysis, 10 (2011), 1257.
doi: 10.3934/cpaa.2011.10.1257. |
[10] |
R. M. Martins and M. A. Teixeira, Reversible-equivariant systems and matricial equations,, Anais da Academia Brasileira de Ci\^encias, 83 (2011), 1.
doi: 10.1590/S0001-37652011000200003. |
[11] |
J. C. van der Meer, "The Hamiltonian Hopf Bifurcation,", Lecture Notes in Mathematics, 1160 (1982).
|
[12] |
J. C. van der Meer, J. A. Sanders and A. Vanderbauwhede, "Hamiltonian Structure of the Reversible Nonsemisimple 1:1 Resonance,", Dynamics, (1994).
|
[13] |
G. B. Price, On reversible dynamical systems,, Trans. Amer. Math. Soc., 37 (1935), 51.
doi: 10.1090/S0002-9947-1935-1501778-0. |
[14] |
M. B. Sevryuk, The finite-dimensional reversible KAM theory,, Phys. D, 112 (1935), 132.
doi: 10.1016/S0167-2789(97)00207-8. |
[15] |
M. A. Teixeira, Singularities of reversible vector fields,, Phys. D, 100 (1997), 101.
doi: 10.1016/S0167-2789(96)00183-2. |
show all references
References:
[1] |
R. Abraham and J. Marsden, "Foundations of Mechanics,", Benjamin Cummings, (1978).
|
[2] |
F. Antoneli, P. H. Baptistelli, A. P. Dias and M. Manoel, Invariant theory and reversible-equivariant vector fields,, J. Pure Appl. Algebra, 213 (2009), 649.
doi: 10.1016/j.jpaa.2008.08.002. |
[3] |
V. I. Arnold, "Arnold's Problems,", Springer-Verlag, (2004).
|
[4] |
V. I. Arnold, "Geometrical Methods in the Theory of Ordinary Differential Equations,", Fundamental Principles of Mathematical Sciences {\bf 250}. Springer-Verlag, 250 (1998).
|
[5] |
G. D. Birkhoff, Dynamical systems with two degrees of freedom,, Trans. Amer. Math. Soc., 18 (1917), 199.
doi: 10.1090/S0002-9947-1917-1501070-3. |
[6] |
R. L. Devaney, Reversible diffeomorphisms and flows,, Trans. Amer. Math. Soc., 218 (1976), 89.
doi: 10.1090/S0002-9947-1976-0402815-3. |
[7] |
G. Gaeta, Normal forms of reversible dynamical systems,, International Journal of Theoretical Physics, 33 (1994), 1917.
doi: 10.1007/BF00671033. |
[8] |
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.
doi: 10.1007/s10231-006-0036-8. |
[9] |
R. M. Martins and M. A. Teixeira, On the Similarity of Hamiltonian and reversible vector fields in 4D,, Communications on Pure and Applied Analysis, 10 (2011), 1257.
doi: 10.3934/cpaa.2011.10.1257. |
[10] |
R. M. Martins and M. A. Teixeira, Reversible-equivariant systems and matricial equations,, Anais da Academia Brasileira de Ci\^encias, 83 (2011), 1.
doi: 10.1590/S0001-37652011000200003. |
[11] |
J. C. van der Meer, "The Hamiltonian Hopf Bifurcation,", Lecture Notes in Mathematics, 1160 (1982).
|
[12] |
J. C. van der Meer, J. A. Sanders and A. Vanderbauwhede, "Hamiltonian Structure of the Reversible Nonsemisimple 1:1 Resonance,", Dynamics, (1994).
|
[13] |
G. B. Price, On reversible dynamical systems,, Trans. Amer. Math. Soc., 37 (1935), 51.
doi: 10.1090/S0002-9947-1935-1501778-0. |
[14] |
M. B. Sevryuk, The finite-dimensional reversible KAM theory,, Phys. D, 112 (1935), 132.
doi: 10.1016/S0167-2789(97)00207-8. |
[15] |
M. A. Teixeira, Singularities of reversible vector fields,, Phys. D, 100 (1997), 101.
doi: 10.1016/S0167-2789(96)00183-2. |
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