Built on

E. Fermi, J. Pasta, and S. Ulam, Studies of the nonlinear problems I, Los Alamos Report LA-1940, (1955), reprinted in Collected Papers of Enrico Fermi , ed. E. Segre, Vol. II (University of Chicago Press, 1965)
1965
Earlier work this paper cites.
C. Sulem, P.-L. Sulem and H. Frisch, Tracing complex singularities with spectral methods,
1983
Earlier work this paper cites.
G. P. Berman and F. M. Izrailev, The Fermi-Pasta-Ulam problem: 50 years of progress, Chaos 15
2005
Earlier work this paper cites.
P. Bizoń and A. Rostworowski, On weakly turbulent instability of anti-de Sitter space,
Original
2011
Earlier work this paper cites.
O. J. C. Dias, G. T. Horowitz and J. E. Santos, Gravitational turbulent instability of Anti-de Sitter space,
Original
2012
Earlier work this paper cites.
M. Maliborski and A. Rostworowski, Time-periodic solutions in an Einstein AdS–massless-scalar-field system,
Original
2013
Earlier work this paper cites.
A. Buchel, S. L. Liebling and L. Lehner, Boson stars in AdS spacetime,
Original
2013
Earlier work this paper cites.
P. Bizoń and J. Jałmużna, Globally regular instability of A d S 3 AdS_{3} ,
Original
2013
Earlier work this paper cites.
V. Balasubramanian, A. Buchel, S. R. Green, L. Lehner and S. L. Liebling, Holographic thermalization, stability of anti-de Sitter space, and the Fermi-Pasta-Ulam paradox,
Original
2014
Earlier work this paper cites.
B. Craps, O. Evnin and J. Vanhoof, Renormalization group, secular term resummation and AdS (in)stability, JHEP 1410
Original
2014
Earlier work this paper cites.
F. V. Dimitrakopoulos, B. Freivogel, M. Lippert and I. S. Yang, Position space analysis of the AdS (in)stability problem,
Original
2015
Earlier work this paper cites.
N. Kim, Time-periodic solutions of massive scalar fields in dynamical AdS background: perturbative constructions,
Original
2015
Earlier work this paper cites.

Similar

N. Deppe and A. R. Frey, Classes of stable initial data for massless and massive scalars in Anti-de Sitter spacetime,
Original
2015
Cited alongside, same era.
B. Craps, O. Evnin and J. Vanhoof, Renormalization, averaging, conservation laws and AdS (in)stability, JHEP 1501
Original
2015
Cited alongside, same era.
I-S. Yang, Missing top of the AdS resonance structure,
Original
2015
Cited alongside, same era.
P. Basu, C. Krishnan and A. Saurabh, A stochasticity threshold in holography and the instability of AdS,
Original
2015
Cited alongside, same era.
A. Buchel, S. R. Green, L. Lehner and S. L. Liebling, Conserved quantities and dual turbulent cascades in anti-de Sitter spacetime, Phys. Rev. D 91

Then

P. Germain, Z. Hani and L. Thomann, On the continuous resonant equation for NLS: I. Deterministic analysis, J. Math. Pur. App. 105
Original
2016
Later among the works it cites.
P. Germain and L. Thomann, On the high frequency limit of the LLL equation , Quart. Appl. Math. 74
Original
2016
Later among the works it cites.
P. Bizoń and A. Rostworowski, Gravitational turbulent instability of AdS 5 ,
Original
2017
Later among the works it cites.
P. Bizoń, B. Craps, O. Evnin, D. Hunik, V. Luyten and M. Maliborski, Conformal flow on S 3 S^{3} and weak field integrability in AdS 4 , Comm. Math. Phys. 353
Original
2017
Later among the works it cites.
B. Craps, O. Evnin and V. Luyten, Maximally rotating waves in AdS and on spheres,

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2018

Energy returns in global AdS_4

Biasi, Anxo, Craps, Ben, Evnin, Oleg

Understand

Recent studies of the weakly nonlinear dynamics of probe fields in global AdS$_4$ (and of the nonrelativistic limit of AdS resulting in the Gross-Pitaevskii equation) have revealed a number of cases with exact dynamical returns for two-mode initial data.

In this paper, we address the question whether similar exact returns are present in the weakly nonlinear dynamics of gravitationally backreacting perturbations in global AdS$_4$.
In the literature, approximate returns were first pointed out numerically and with limited precision.
We first provide a thorough numerical analysis and discover returns that are so accurate that it would be tantalizing to sign off the small imperfections as an artifact of numerics.