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Periodic orbits for a generalized Friedmann-Robertson-Walker Hamiltonian system in dimension $6$
1. | Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain |
References:
[1] |
R. Abraham and J. E. Marsden, Foundations of Mechanics, Benjamin, Reading, Masachusets, 1978. |
[2] |
C. Belomte, D. Bocaaletti and G. Pucacco, On the orbit structure of the logarithm potential, Astrophys. J., 669 (2007), 202-217. |
[3] |
E. Calzeta and C. E. Hasi, Chaotic Friedmann-Robertson-Walker cosmology, Class. Quantum Gravity, 10 (1993), 1825-1841.
doi: 10.1088/0264-9381/10/9/022. |
[4] |
S. W. Hawkings, Arrow of time in cosmology, Phys. Rev. D, 32 (1985), 2489-2495.
doi: 10.1103/PhysRevD.32.2489. |
[5] |
F. Lembarki and J. Llibre, Periodic orbits for the generalized Yang-Mills Hamiltonian system in dimension $6$, Nonlinear Dyn., 76 (2014), 1807-1819.
doi: 10.1007/s11071-014-1249-9. |
[6] |
J. Llibre and A. Makhlouf, Periodic orbits of the generalized Friedmann-Robertson-Walker Hamiltonian systems, Astrophys, 344 (2013), 46-50. |
[7] |
D. Merrit and M. Valluri, Chaos and mixing in triaxial stellar systems, Astrophys, 471 (1996), 82-105. |
[8] |
D. Page, Will entroy decrease if the universe recollapses?, Phys. Rev. D, 32 (1991), 2496-2499.
doi: 10.1103/PhysRevD.32.2496. |
[9] |
Y. Papaphilippou and J. Laskar, Frequency map analysis and global dynamics in a galactic potential with two degrees of freedom, Astron. Astrophys., 307 (1996), 427-449. |
[10] |
Y. Papaphilippou and J. Laskar, Global dynamics of triaxial galactic models though frequency analysis, Astron. Astrophys., 329 (1998), 451-481. |
[11] |
G. Pucacco, D. Boccaletti and C. Belmonte, Quantitative predictions with detuned normal forms, Celest. Mech. Dyn. Astron., 102 (2008), 163-176.
doi: 10.1007/s10569-008-9141-x. |
[12] |
F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Universitext, Springer-Verlag, 1996.
doi: 10.1007/978-3-642-61453-8. |
[13] |
H. S. Zhao, C. M. Carollo and T. De Zeeuw, Can galactic nuclei be non-axisymmetric? The parameter space of power-law discs, Mon. Not. R. Astron. Soc., 304 (1999), 457-464. |
show all references
References:
[1] |
R. Abraham and J. E. Marsden, Foundations of Mechanics, Benjamin, Reading, Masachusets, 1978. |
[2] |
C. Belomte, D. Bocaaletti and G. Pucacco, On the orbit structure of the logarithm potential, Astrophys. J., 669 (2007), 202-217. |
[3] |
E. Calzeta and C. E. Hasi, Chaotic Friedmann-Robertson-Walker cosmology, Class. Quantum Gravity, 10 (1993), 1825-1841.
doi: 10.1088/0264-9381/10/9/022. |
[4] |
S. W. Hawkings, Arrow of time in cosmology, Phys. Rev. D, 32 (1985), 2489-2495.
doi: 10.1103/PhysRevD.32.2489. |
[5] |
F. Lembarki and J. Llibre, Periodic orbits for the generalized Yang-Mills Hamiltonian system in dimension $6$, Nonlinear Dyn., 76 (2014), 1807-1819.
doi: 10.1007/s11071-014-1249-9. |
[6] |
J. Llibre and A. Makhlouf, Periodic orbits of the generalized Friedmann-Robertson-Walker Hamiltonian systems, Astrophys, 344 (2013), 46-50. |
[7] |
D. Merrit and M. Valluri, Chaos and mixing in triaxial stellar systems, Astrophys, 471 (1996), 82-105. |
[8] |
D. Page, Will entroy decrease if the universe recollapses?, Phys. Rev. D, 32 (1991), 2496-2499.
doi: 10.1103/PhysRevD.32.2496. |
[9] |
Y. Papaphilippou and J. Laskar, Frequency map analysis and global dynamics in a galactic potential with two degrees of freedom, Astron. Astrophys., 307 (1996), 427-449. |
[10] |
Y. Papaphilippou and J. Laskar, Global dynamics of triaxial galactic models though frequency analysis, Astron. Astrophys., 329 (1998), 451-481. |
[11] |
G. Pucacco, D. Boccaletti and C. Belmonte, Quantitative predictions with detuned normal forms, Celest. Mech. Dyn. Astron., 102 (2008), 163-176.
doi: 10.1007/s10569-008-9141-x. |
[12] |
F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Universitext, Springer-Verlag, 1996.
doi: 10.1007/978-3-642-61453-8. |
[13] |
H. S. Zhao, C. M. Carollo and T. De Zeeuw, Can galactic nuclei be non-axisymmetric? The parameter space of power-law discs, Mon. Not. R. Astron. Soc., 304 (1999), 457-464. |
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