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Normally stable hamiltonian systems
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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), 158-186.
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), 1237-1258. |
[3] |
R. L. Devaney, Reversible diffeomorphisms and flows, Trans. Am. Math. Soc., 218 (1976), 89-113.
doi: 10.1090/S0002-9947-1976-0402815-3. |
[4] |
J. Hale, "Ordinary Differential Equations," $1^{st}$ edition, New York, Wiley-Interscience, 1969. |
[5] |
G. Iooss and M. Adelmeyer, "Topics in Bifurcation Theory and Applications," Adv. Ser. Nonlinear Dynamics, 3, World Scientific Publishing Co., Inc., River Edge, NJ, 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), 105-117. |
[7] |
J. S. W. Lamb and J. A. G. Roberts, Time-reversal symmetry in dynamical systems: a survey, Phys. D, 112 (1998), 1-39. |
[8] |
M. F. S. Lima and M. Teixeira, Families of periodic orbits in resonant reversible systems, Bull. Braz. Math. Soc., 40 (2009), 521-547.
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), 569-584.
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, University Ilmenau, Germany, 1999. |
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), 158-186.
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), 1237-1258. |
[3] |
R. L. Devaney, Reversible diffeomorphisms and flows, Trans. Am. Math. Soc., 218 (1976), 89-113.
doi: 10.1090/S0002-9947-1976-0402815-3. |
[4] |
J. Hale, "Ordinary Differential Equations," $1^{st}$ edition, New York, Wiley-Interscience, 1969. |
[5] |
G. Iooss and M. Adelmeyer, "Topics in Bifurcation Theory and Applications," Adv. Ser. Nonlinear Dynamics, 3, World Scientific Publishing Co., Inc., River Edge, NJ, 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), 105-117. |
[7] |
J. S. W. Lamb and J. A. G. Roberts, Time-reversal symmetry in dynamical systems: a survey, Phys. D, 112 (1998), 1-39. |
[8] |
M. F. S. Lima and M. Teixeira, Families of periodic orbits in resonant reversible systems, Bull. Braz. Math. Soc., 40 (2009), 521-547.
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), 569-584.
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, University Ilmenau, Germany, 1999. |
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