R. P. Agarwal and D. O-'regan, Ordinary and Partial Differential Equations (With Special Functions, Fourier Series, and Boundary Value Problems, 2009.

P. Augustova and Z. Beran, Characteristics of the Chen attractor Nostradamus 2013 : Prediction, Modeling and Analysis of Complex Systems, Advances in Intelligent Systems and Computing, pp.305-312, 2013.

J. C. Butcher, Numerical Methods for Ordinary Differential Equations, 2003.

G. Chen and T. Ueta, YET ANOTHER CHAOTIC ATTRACTOR, International Journal of Bifurcation and Chaos, vol.09, issue.07, pp.1465-1466, 1999.
DOI : 10.1142/S0218127499001024

Z. Galias and W. Tucker, Is the H??non attractor chaotic?, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.25, issue.3, pp.33102-33103, 2015.
DOI : 10.1063/1.4913945

A. Gibbons, A Program for the Automatic Integration of Differential Equations using the Method of Taylor Series, The Computer Journal, vol.3, issue.2, pp.108-111, 1960.
DOI : 10.1093/comjnl/3.2.108

E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I : Nonstiff Problems, 1993.
DOI : 10.1007/978-3-662-12607-3

M. Henon, A two-dimensional mapping with a strange attractor, Communications in Mathematical Physics, vol.20, issue.1, pp.69-77, 1976.
DOI : 10.1007/BF01608556

P. Holoborodko, The High-Performance C++ Interface for MPFR Library, 2015.

D. A. Kaloshin, Search for and stabilization of unstable saddle cycles in the Lorenz system, Differential Equations, vol.37, issue.11, pp.1636-1639, 2001.
DOI : 10.1023/A:1017933202944

E. N. Lorenz, Deterministic Nonperiodic Flow, Journal of the Atmospheric Sciences, vol.20, issue.2, pp.130-141, 1963.
DOI : 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2

R. Lozi, Can we trust in numerical computations of chaotic solutions of dynamical systems ?, World Scientific Series in Nonlinear Science Series A, vol.84, pp.63-98, 2013.
DOI : 10.1142/9789814434867_0004
URL : https://hal.archives-ouvertes.fr/hal-00682818

A. N. Pchelintsev, On constructing generally periodic solutions of a complicated structure of a non-autonomous system of differential equations, Numerical Analysis and Applications, vol.6, issue.1, pp.54-61, 2013.
DOI : 10.1134/S1995423913010072

A. N. Pchelintsev, Numerical and physical modeling of the dynamics of the Lorenz system, Numerical Analysis and Applications, vol.7, issue.2, pp.159-167, 2014.
DOI : 10.1134/S1995423914020098

C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, 1982.
DOI : 10.1007/978-1-4612-5767-7

W. Tucker, The Lorenz attractor exists Comptes-Rendus de l, Academie des Sciences, vol.328, pp.1197-1202, 1999.

W. Tucker, A Rigorous ODE Solver and Smale???s 14th Problem, Foundations of Computational Mathematics, vol.2, issue.1, pp.53-117, 2002.
DOI : 10.1007/s002080010018

T. Ueta and G. Chen, Bifurcation analysis of Chen's attractor, Int. J. Bifurcation and Chaos, vol.10, pp.1917-1931, 2000.

J. A. Yorke and E. D. Yorke, Metastable chaos: The transition to sustained chaotic behavior in the Lorenz model, Journal of Statistical Physics, vol.4, issue.1, pp.263-277, 1979.
DOI : 10.1007/BF01011469