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On the stability of the Lagrangian homographic solutions in a curved three-body problem on $\mathbb{S}^2$
Reversibility and branching of periodic orbits
1. | Departamento de Física, Química e Matemática, Universidade Federal de São Carlos, 18052-780, S.P., Brazil |
2. | Departamento de Matemática, Universidade Estadual de Campinas, Caixa Postal 6065, 13083-970, Campinas, S.P., Brazil |
References:
[1] |
A. R. Champneys, Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics,, Physica D, 112 (1998), 158.
doi: 10.1016/S0167-2789(97)00209-1. |
[2] |
J. V. Chaparova, L. A. Peletier and S. A. Tersian, Existence and nonexistence of nontrivial solutions of semilinear fourth- and sixth-order differential equations,, Advances in Differential Equations, 8 (2003), 1237.
|
[3] |
R. L. Devaney, Reversible diffeomorphisms and flows,, Trans. Am. Math. Soc., 218 (1976), 89.
doi: 10.1090/S0002-9947-1976-0402815-3. |
[4] |
J. Hale, "Ordinary Differential Equations,", $1^{st}$ edition, (1969).
|
[5] |
G. Iooss and M. Adelmeyer, "Topics in Bifurcation Theory and Applications,", Adv. Ser. Nonlinear Dynamics, 3 (1992).
|
[6] |
A. Jacquemard, M. F. S. Lima and M. Teixeira, Degenerate resonances and branching of periodic orbits,, Annali di Matematica ed Applicata, 187 (1992), 105.
|
[7] |
J. S. W. Lamb and J. A. G. Roberts, Time-reversal symmetry in dynamical systems: a survey,, Phys. D, 112 (1998), 1.
|
[8] |
M. F. S. Lima and M. Teixeira, Families of periodic orbits in resonant reversible systems,, Bull. Braz. Math. Soc., 40 (2009), 521.
doi: 10.1007/s00574-009-0025-9. |
[9] |
C. W. Shih, Bifurcations of Symmetric Periodic Orbits near Equilibrium in Reversible Systems,, Int. J. Bifurcation and Chaos, 7 (1997), 569.
doi: 10.1142/S0218127497000406. |
[10] |
T. Wagenknecht, "An analytical Study of a Two Degrees of Freedom Hamiltonian System Associated the Reversible Hyperbolic Umbilic,", Ph. D thesis, (1999). Google Scholar |
show all references
References:
[1] |
A. R. Champneys, Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics,, Physica D, 112 (1998), 158.
doi: 10.1016/S0167-2789(97)00209-1. |
[2] |
J. V. Chaparova, L. A. Peletier and S. A. Tersian, Existence and nonexistence of nontrivial solutions of semilinear fourth- and sixth-order differential equations,, Advances in Differential Equations, 8 (2003), 1237.
|
[3] |
R. L. Devaney, Reversible diffeomorphisms and flows,, Trans. Am. Math. Soc., 218 (1976), 89.
doi: 10.1090/S0002-9947-1976-0402815-3. |
[4] |
J. Hale, "Ordinary Differential Equations,", $1^{st}$ edition, (1969).
|
[5] |
G. Iooss and M. Adelmeyer, "Topics in Bifurcation Theory and Applications,", Adv. Ser. Nonlinear Dynamics, 3 (1992).
|
[6] |
A. Jacquemard, M. F. S. Lima and M. Teixeira, Degenerate resonances and branching of periodic orbits,, Annali di Matematica ed Applicata, 187 (1992), 105.
|
[7] |
J. S. W. Lamb and J. A. G. Roberts, Time-reversal symmetry in dynamical systems: a survey,, Phys. D, 112 (1998), 1.
|
[8] |
M. F. S. Lima and M. Teixeira, Families of periodic orbits in resonant reversible systems,, Bull. Braz. Math. Soc., 40 (2009), 521.
doi: 10.1007/s00574-009-0025-9. |
[9] |
C. W. Shih, Bifurcations of Symmetric Periodic Orbits near Equilibrium in Reversible Systems,, Int. J. Bifurcation and Chaos, 7 (1997), 569.
doi: 10.1142/S0218127497000406. |
[10] |
T. Wagenknecht, "An analytical Study of a Two Degrees of Freedom Hamiltonian System Associated the Reversible Hyperbolic Umbilic,", Ph. D thesis, (1999). Google Scholar |
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