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E. Fermi, J. Pasta, and S. M. Ulam, Studies of nonlinear problems. I , Technical Report LA-1940 (1955) also in Enrico Fermi: Collected Papers, volume 2
1965
Earlier work this paper cites.
C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman, San Francisco, 1973)
1973
Earlier work this paper cites.
I. Gradshteyn and I. Ryzhik, “Table of integrals, series, and products,” (Academic Press Inc., 1980) 4th ed
1980
Earlier work this paper cites.
H. Friedrich, Journal of Geometry and Physics 3
1986
Earlier work this paper cites.
R. Cooke and V. I. Arnol’d, Ordinary Differential Equations , Springer Textbook (Springer Berlin Heidelberg, 1992)
1992
Earlier work this paper cites.
A. Lichtenberg and M. Lieberman, Regular and chaotic dynamics , Applied mathematical sciences (Springer-Verlag, 1992)
1992
Earlier work this paper cites.
D. Christodoulou and S. Klainerman, Séminaire Équations aux dérivées partielles (Polytechnique) , 1 (1993)
1993
Earlier work this paper cites.
S. Flach, M. Ivanchenko, and O. Kanakov, Phys. Rev. Lett. 95
2005
Earlier work this paper cites.
M. T. Anderson, Class.Quant.Grav. 23
2006
Earlier work this paper cites.
S. Flach, M. Ivanchenko, and O. Kanakov, Phys. Rev. E 73
2006
Earlier work this paper cites.
P. Bizon and A. Rostworowski, Phys. Rev. Lett. 107
Original
2011
Earlier work this paper cites.

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2015

Green, Stephen R., Maillard, Antoine, Lehner, Luis et al.

We study the stability of anti-de Sitter (AdS) spacetime to spherically symmetric perturbations of a real scalar field in general relativity.

Further, we work within the context of the "two time framework" (TTF) approximation, which describes the leading nonlinear effects for small amplitude perturbations, and is therefore suitable for studying the weakly turbulent instability of AdS---including both collapsing and non-collapsing solutions.
We have previously identified a class of quasi-periodic (QP) solutions to the TTF equations, and in this work we analyze their stability.
We show that there exist several families of QP solutions that are stable to linear order, and we argue that these solutions represent islands of stability in TTF.

E. Fermi, J. Pasta, and S. M. Ulam, Studies of nonlinear problems. I , Technical Report LA-1940 (1955) also in Enrico Fermi: Collected Papers, volume 2
1965
Earlier work this paper cites.
C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman, San Francisco, 1973)
1973
Earlier work this paper cites.
I. Gradshteyn and I. Ryzhik, “Table of integrals, series, and products,” (Academic Press Inc., 1980) 4th ed
1980
Earlier work this paper cites.
H. Friedrich, Journal of Geometry and Physics 3
1986
Earlier work this paper cites.
R. Cooke and V. I. Arnol’d, Ordinary Differential Equations , Springer Textbook (Springer Berlin Heidelberg, 1992)
1992
Earlier work this paper cites.
A. Lichtenberg and M. Lieberman, Regular and chaotic dynamics , Applied mathematical sciences (Springer-Verlag, 1992)
1992
Earlier work this paper cites.
D. Christodoulou and S. Klainerman, Séminaire Équations aux dérivées partielles (Polytechnique) , 1 (1993)
1993
Earlier work this paper cites.
S. Flach, M. Ivanchenko, and O. Kanakov, Phys. Rev. Lett. 95
2005
Earlier work this paper cites.
M. T. Anderson, Class.Quant.Grav. 23
2006
Earlier work this paper cites.
S. Flach, M. Ivanchenko, and O. Kanakov, Phys. Rev. E 73
2006
Earlier work this paper cites.
P. Bizon and A. Rostworowski, Phys. Rev. Lett. 107
Original
2011
Earlier work this paper cites.