D. G. Andrews and . Mcintyre, Generalized eliassen-palm and charney-drazin theorems for waves on axismmetric mean flows in compressible atmospheres, Journal of the Atmospheric Sciences, vol.35, issue.2, pp.175-185, 1978.

L. Bachelier, Théorie de la spéculation, 1900.

N. Bakas and P. Ioannou, A theory for the emergence of coherent structures in beta-plane turbulence, 2013.

R. Balian, Du microscopique au macroscopique: cours de physique statistique de l'École polytechnique. Ecole Polytech, 1982.

K. Batygin and G. Laughlin, On the dynamical stability of the solar system, The Astrophysical Journal, vol.683, issue.2, p.1207, 2008.

K. Batygin, A. Morbidelli, and M. Holman, Chaotic disintegration of the inner solar system, The Astrophysical Journal, vol.799, issue.2, p.120, 2015.

M. Berry, Regular and irregular motion, AIP Conference proceedings, vol.46, pp.16-120, 1978.

G. Boffetta and . Robert-e-ecke, Two-dimensional turbulence, Annual Review of Fluid Mechanics, vol.44, pp.427-451, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00283891

F. Bouchet and T. Grafke, Tomás Tangarife, and Eric Vanden-Eijnden. Large deviations in fast-slow systems, Journal of Statistical Physics, vol.162, issue.4, pp.793-812, 2016.

F. Bouchet and H. Morita, Large time behavior and asymptotic stability of the 2d euler and linearized euler equations, Physica D: Nonlinear Phenomena, vol.239, issue.12, pp.948-966, 2010.

F. Bouchet, C. Nardini, and T. Tangarife, Kinetic theory of jet dynamics in the stochastic barotropic and 2d navier-stokes equations, Journal of Statistical Physics, vol.153, issue.4, pp.572-625, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00819779

F. Bouchet, C. Nardini, and T. Tangarife, Kinetic theory and quasilinear theories of jet dynamics, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01266458

F. Bouchet and E. Simonnet, Random changes of flow topology in two-dimensional and geophysical turbulence, Physical review letters, vol.102, issue.9, p.94504, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00273264

G. Boué, J. Laskar, and F. Farago, A simple model of the chaotic eccentricity of mercury, Astronomy & Astrophysics, vol.548, p.43, 2012.

D. Brouwer, On the accumulation of errors in numerical integration, The Astronomical Journal, vol.46, pp.149-153, 1937.

B. Caroli, B. Caroli, and . Roulet, Diffusion in a bistable potential: The functional integral approach, Journal of Statistical Physics, vol.26, issue.1, pp.83-111, 1981.

. Boris-v-chirikov, A universal instability of many-dimensional oscillator systems, Physics reports, vol.52, issue.5, pp.263-379, 1979.

C. Navid and . Constantinou, Formation of large-scale structures by turbulence in rotating planets, 2015.

C. Navid, . Constantinou, J. Petros, B. F. Ioannou, and . Farrell, Emergence and equilibration of jets in beta-plane turbulence, 2012.

C. M. Alexandre, J. Correia, and . Laskar, The four final rotation states of venus, Nature, vol.411, issue.6839, p.767, 2001.

J. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attractors, The Theory of Chaotic Attractors, pp.273-312, 1985.
DOI : 10.1142/9789812833709_0025

.. J. Jp-eckmann, rev. mod. phys, vol.57, p.617, 1985.

F. Brian, P. Farrell, and . Ioannou, Structure and spacing of jets in barotropic turbulence, Journal of the Atmospheric Sciences, vol.64, issue.10, pp.3652-3665, 2007.

A. Fienga, . Laskar, H. Morley, . Manche, C. Kuchynka et al., Inpop08, a 4-d planetary ephemeris: from asteroid and time-scale computations to esa mars express and venus express contributions, Astronomy & Astrophysics, vol.507, issue.3, pp.1675-1686, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00472471

M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems, 2012.

Y. Fu and J. Laskar, Frequency analysis and the representation of slowly diffusing planetary solutions, 2017.

G. Gallavoti, Chaotic hypothesis, vol.3, p.5906

G. Gallavotti and E. Cohen, Dynamical ensembles in stationary states, Journal of Statistical Physics, vol.80, issue.5, pp.931-970, 1995.

B. Galperin, S. Sukoriansky, and H. Huang, Universal n-5 spectrum of zonal flows on giant planets, Physics of Fluids, vol.13, issue.6, pp.1545-1548, 1994.

B. Galperin, M. B. Roland, S. Young, N. Sukoriansky, . Dikovskaya et al., Cassini observations reveal a regime of zonostrophic macroturbulence on jupiter, Icarus, vol.229, pp.295-320, 2014.

R. García-herrera, J. Díaz, R. M. Trigo, J. Luterbacher, and E. M. Fischer, A review of the european summer heat wave of, Critical Reviews in Environmental Science and Technology, vol.40, issue.4, pp.267-306, 2003.

C. W. Gardiner, Handbook of stochastic methods for physics, chemistry and the natural sciences, Springer Series in Synergetics, 1994.

A. E. Gill, Atmosphere-ocean dynamics, vol.30, 1982.

L. Seymour, H. A. Hess, and . Panofsky, The atmospheres of the other planets, Compendium of meteorology, pp.391-398, 1951.

J. Idier, Traitement numérique du signal. deuxième partie: algorithmes, 2004.

P. Andrew and . Ingersoll, Atmospheric dynamics of the outer planets, Science, vol.248, issue.4953, pp.308-315, 1990.

R. F. Andrew-p-ingersoll, J. L. Beebe, G. W. Mitchell, . Garneau, J. Gary-m-yagi et al., Interaction of eddies and mean zonal flow on jupiter as inferred from voyager 1 and 2 images, Journal of Geophysical Research A, vol.86, issue.A10, pp.8733-8743, 1981.

T. Ishihara, T. Gotoh, and Y. Kaneda, Study of high-reynolds number isotropic turbulence by direct numerical simulation, Annual Review of Fluid Mechanics, vol.41, pp.165-180, 2009.
DOI : 10.1146/annurev.fluid.010908.165203

Y. Kaspi, . Galanti, D. J. Hubbard, . Stevenson, L. Sj-bolton et al., Jupiter's atmospheric jet streams extend thousands of kilometres deep, Nature, vol.555, issue.7695, p.223, 2018.
DOI : 10.1038/nature25793

D. Kelly and I. Melbourne, Smooth approximation of stochastic differential equations. The Annals of Probability, vol.44, pp.479-520, 2016.
DOI : 10.1214/14-aop979

URL : http://arxiv.org/pdf/1403.7281.pdf

R. Khasminskii, On an averaging principle for ito stochastic differential equations, Kybernetika, vol.4, pp.260-279, 1968.

Y. Kifer, Averaging principle for fully coupled dynamical systems and large deviations, vol.24, pp.847-871, 2004.

Y. Kifer, Large deviations and adiabatic transitions for dynamical systems and Markov processes in fully coupled averaging, 2009.
DOI : 10.1090/memo/0944

URL : http://arxiv.org/pdf/0710.2405v1.pdf

M. Kimoto and M. Ghil, Multiple flow regimes in the northern hemisphere winter. part i: Methodology and hemispheric regimes, Journal of the Atmospheric Sciences, vol.50, issue.16, pp.2625-2644, 1993.

T. Khanh-dang-nguyen, J. Lam, and . Kurchan, Stochastic perturbation of integrable systems: a window to weakly chaotic systems, Journal of Statistical Physics, vol.156, issue.4, pp.619-646, 2014.

J. Laskar, A numerical experiment on the chaotic behaviour of the solar system, Nature, vol.338, issue.6212, p.237, 1989.

J. Laskar, The chaotic motion of the solar system: a numerical estimate of the size of the chaotic zones, Icarus, vol.88, issue.2, pp.266-291, 1990.

J. Laskar, Frequency analysis for multi-dimensional systems. global dynamics and diffusion, Physica D: Nonlinear Phenomena, vol.67, issue.1-3, pp.257-281, 1993.

J. Laskar, Large-scale chaos in the solar system, Astronomy and Astrophysics, vol.287, pp.9-12, 1994.
DOI : 10.1007/978-94-009-0307-4_10

J. Laskar, Large scale chaos and marginal stability in the solar system, Celestial Mechanics and Dynamical Astronomy, vol.64, issue.1-2, pp.115-162, 1996.
DOI : 10.1007/978-94-009-0307-4_10

J. Laskar, Large scale chaos and the spacing of the inner planets, Astronomy and Astrophysics, vol.317, pp.75-78, 1997.

J. Laskar, Chaotic diffusion in the solar system, Icarus, vol.196, issue.1, pp.1-15, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00258631

J. Laskar, , 2009.

J. Laskar and G. Boué, Explicit expansion of the three-body disturbing function for arbitrary eccentricities and inclinations, Astronomy & Astrophysics, vol.522, p.60, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00619707

J. Laskar, A. Fienga, M. Gastineau, and H. Manche, La2010: a new orbital solution for the long-term motion of the earth, Astronomy & Astrophysics, vol.532, p.89, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00622971

J. Laskar, C. Froeschlé, and A. Celletti, The measure of chaos by the numerical analysis of the fundamental frequencies. application to the standard mapping, Physica D: Nonlinear Phenomena, vol.56, issue.2-3, pp.253-269, 1992.

J. Laskar and M. Gastineau, Existence of collisional trajectories of mercury, mars and venus with the earth, Nature, vol.459, issue.7248, p.817, 2009.

J. Laskar and M. Gastineau, Existence of collisional trajectories of mercury, mars and venus with the earth, Nature, vol.459, issue.7248, pp.817-819, 2009.

J. Laskar, M. Gastineau, and . Mercure, , 2009.

J. Laskar, M. Gastineau, and J. Delisle, Strong chaos induced by close encounters with ceres and vesta, Ariadna Farrés, and Agnes Fienga, vol.532, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00733676

J. Laskar and A. Petit, Amd-stability and the classification of planetary systems, Astronomy & Astrophysics, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02178940

J. Laskar and P. Robutel, The chaotic obliquity of the planets, Nature, vol.361, issue.6413, pp.608-612, 1993.

J. Laskar and P. Robutel, Stability of the planetary three-body problem, Celestial Mechanics and Dynamical Astronomy, vol.62, issue.3, pp.193-217, 1995.

J. Laskar, P. Robutel, F. Joutel, M. Gastineau, A. Correia et al., A long-term numerical solution for the insolation quantities of the earth, Astronomy & Astrophysics, vol.428, issue.1, pp.261-285, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00001603

T. Lestang, F. Ragone, C. Bréhier, C. Herbert, and F. Bouchet, Computing return times or return periods with rare event algorithms, Journal of Statistical Mechanics: Theory and Experiment, vol.2018, issue.4, p.43213, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02070403

G. Li and K. Batygin, On the spin-axis dynamics of a moonless earth, The Astrophysical Journal, vol.790, issue.1, p.69, 2014.

L. Li, P. Andrew, X. Ingersoll, and . Huang, Interaction of moist convection with zonal jets on jupiter and saturn, Icarus, vol.180, issue.1, pp.113-123, 2006.

J. Allan, . Lichtenberg, and . Michael-a-lieberman, Regular and stochastic motion, vol.38, 2013.

J. Jack, J. W. Lissauer, J. E. Barnes, and . Chambers, Obliquity variations of a moonless earth, Icarus, vol.217, issue.1, pp.77-87, 2012.

Y. Lithwick and Y. Wu, Theory of secular chaos and mercury's orbit, The Astrophysical Journal, vol.739, issue.1, p.31, 2011.

A. Morbidelli, Modern celestial mechanics: aspects of solar system dynamics, 2002.

A. Morbidelli and A. Giorgilli, Superexponential stability of kam tori, Journal of statistical physics, vol.78, pp.1607-1617, 1995.

A. Morbidelli and A. Giorgilli, On the role of high order resonances in normal forms and in separatrix splitting, Physica D: Nonlinear Phenomena, vol.102, issue.3-4, pp.195-207, 1997.

D. Carl, . Murray, and . Stanley-f-dermott, Solar system dynamics, 1999.

N. N. Nekhoroshev, An exponential estimate of the time of stability of nearly-integrable hamiltonian systems, Russian Mathematical Surveys, vol.32, issue.6, pp.1-65, 1977.

T. Nemoto, F. Bouchet, R. L. Jack, and V. Lecomte, Populationdynamics method with a multicanonical feedback control, Physical Review E, vol.93, issue.6, p.62123, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01396562

J. Olivier-néron-de-surgy and . Laskar, On the long term evolution of the spin of the earth, Astronomy and Astrophysics, vol.318, pp.975-989, 1997.

A. Grigorios, A. Pavliotis, and . Stuart, Multiscale methods: averaging and homogenization, 2008.

J. Pedlosky, Geophysical fluid dynamics. New York and Berlin, 1982.

C. Carolyn, . Porco, A. Robert, A. West, A. Mcewen et al., Cassini imaging of jupiter's atmosphere, satellites, and rings, Science, vol.299, issue.5612, pp.1541-1547, 2003.

F. Ragone, J. Wouters, and F. Bouchet, Computation of extreme heat waves in climate models using a large deviation algorithm, Proceedings of the National Academy of Sciences, p.201712645, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01584944

J. Robine, S. Lan, K. Cheung, S. L. Roy, H. Van-oyen et al., Death toll exceeded 70,000 in europe during the summer of, Comptes Rendus Biologies, vol.331, issue.2, pp.171-178, 2003.

. John-h-rogers, The giant planet Jupiter, vol.6, 1995.

J. Rolland, F. Bouchet, and E. Simonnet, Computing transition rates for the 1-d stochastic ginzburgâlandauâallenâcahn equation for finite-amplitude noise with a rare event algorithm, Journal of Statistical Physics, vol.162, issue.2, pp.277-311, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01178526

D. Ruelle, Measures describing a turbulent flow, Annals of the New York Academy of Sciences, vol.357, issue.1, pp.1-9, 1980.

C. Salyk, P. Andrew, J. Ingersoll, A. Lorre, A. Vasavada et al., Interaction between eddies and mean flow in jupiter's atmosphere: Analysis of cassini imaging data, Icarus, vol.185, issue.2, pp.430-442, 2006.

J. M. Sancho, D. San-miguel, and . Dürr, Adiabatic elimination for systems of brownian particles with nonconstant damping coefficients, Journal of Statistical Physics, vol.28, issue.2, pp.291-305, 1982.

T. Schneider and J. Liu, Formation of Jets and Equatorial Superrotation on Jupiter, Journal of Atmospheric Sciences, vol.66, p.579, 2009.

C. Simó, On the analytical and numerical approximation of invariant manifolds, Les Méthodes Modernes de la Mécanique Céleste. Modern methods in celestial mechanics, pp.285-329, 1990.

Y. Grigor and &. Sinai, Dynamical systems with elastic reflections, Russian Mathematical Surveys, vol.25, issue.2, pp.137-189, 1970.

K. Srinivasan and . Young, Reynolds stress and eddy diffusivity of ?-plane shear flows, Journal of the Atmospheric Sciences, vol.71, issue.6, pp.2169-2185, 2014.

G. J. Sussman and J. Wisdom, Chaotic evolution of the solar system, Science, vol.257, issue.5066, p.56, 1992.

T. Tangarife, Kinetic theory and large deviations for the dynamics of geophysical flows, 2015.
URL : https://hal.archives-ouvertes.fr/tel-01241523

H. Touchette, The large deviation approach to statistical mechanics, Physics Reports, vol.478, issue.1-3, pp.1-69, 2009.

J. R. Touma, M. V. Tremaine, and . Kazandjian, Gauss's method for secular dynamics, softened, Monthly Notices of the Royal Astronomical Society, vol.394, issue.2, pp.1085-1108, 2009.

M. Vallikivi, B. Ganapathisubramani, and A. J. Smits, Spectral scaling in boundary layers and pipes at very high reynolds numbers, Journal of Fluid Mechanics, vol.771, pp.303-326, 2015.

R. Ashwin, A. Vasavada, and . Showman, Jovian atmospheric dynamics: An update after galileo and cassini, Reports on Progress in Physics, vol.68, issue.8, p.1935, 2005.

Y. Veretennikov, On large deviations in the averaging principle for sdes with a" full dependence, Annals of probability, pp.284-296, 1999.

A. Vulpiani, F. Cecconi, M. Cencini, A. Puglisi, and D. Vergni, Large deviations in physics. The Legacy of the Law of Large Numbers, 2014.

H. Wanner, S. Brönnimann, C. Casty, D. Gyalistras, J. Luterbacher et al., North atlantic oscillationconcepts and studies, Surveys in geophysics, vol.22, issue.4, pp.321-381, 2001.

E. Woillez and F. Bouchet, Long-term influence of asteroids on planet longitudes and chaotic dynamics of the solar system, Astronomy & Astrophysics, vol.607, p.62, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01558510

E. Woillez and F. Bouchet, Theoretical prediction of reynolds stresses and velocity profiles for barotropic turbulent jets, Europhysics Letters), vol.118, issue.5, p.54002, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01357478

P. K. Yeung, . Zhai, and . Sreenivasan, Extreme events in computational turbulence, Proceedings of the National Academy of Sciences, vol.112, issue.41, pp.12633-12638, 2015.

A. Youssef, . Philip, and . Marcus, The dynamics of jovian white ovals from formation to merger, Icarus, vol.162, issue.1, pp.74-93, 2003.

M. V. Zagarola and A. J. Smits, Scaling of the mean velocity profile for turbulent pipe flow, Physical review letters, vol.78, issue.2, p.239, 1997.