A. A. Agrachev and R. V. Gamkrelidze, Chronological algebras and nonstationary vector fields, Journal of Soviet Mathematics, vol.15, issue.2, pp.1650-1675, 1981.
DOI : 10.1007/BF01084595

N. Bergeron and J. Loday, The symmetric operation in a free pre-Lie algebra is magmatic, Proc. AMS, pp.1585-1597, 2011.
DOI : 10.1090/S0002-9939-2010-10813-4

D. Calaque, K. Ebrahimi-fard, and D. Manchon, Two interacting Hopf algebras of trees: A Hopf-algebraic approach to composition and substitution of B-series, Advances in Applied Mathematics, vol.47, issue.2, pp.282-308, 2011.
DOI : 10.1016/j.aam.2009.08.003
URL : https://hal.archives-ouvertes.fr/hal-00288313

A. Cayley, On the theory of Analytic Forms called trees, Philos. Mag, vol.133, pp.242-246, 1857.

F. Chapoton, Rooted trees and an exponential-like series. arxiv :math, pp.209104-209105, 2002.

F. Chapoton, Operads and algebraic combinatorics of trees, Sém. Loth. Combinatoire, vol.58, 2008.

F. Chapoton and M. Livernet, Pre-Lie algebras and the rooted trees operad, Int. Math. Res. Not, pp.395-408, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00002110

. Ph, E. Chartier, G. Hairer, and . Vilmart, Numerical integrators based on modified differential equations, Math.Comp, vol.76, pp.1941-1953, 2007.

A. Connes and D. Kreimer, Hopf Algebras, Renormalization and Noncommutative Geometry, Communications in Mathematical Physics, vol.199, issue.1, pp.203-242, 1998.
DOI : 10.1007/s002200050499

J. Dixmier, Algèbres enveloppantes, Gauthier-Villars, 1974.

A. Dzhumadl-'daev and C. , Trees, free right-symmetric algebras, free Novikov algebras and identities, Homotopy, Homology and Applications, pp.165-190, 2002.

V. Dotsenko, An operadic approach to deformation quantization of compatible Poisson brackets, I, Journal of Generalized Lie Theory and Applications, vol.1, issue.2, pp.107-115, 2007.
DOI : 10.4303/jglta/S070203

L. Foissy, Les alg??bres de Hopf des arbres enracin??s d??cor??s, II, Bulletin des Sciences Math??matiques, vol.126, issue.4, pp.193-239, 2002.
DOI : 10.1016/S0007-4497(02)01113-2

M. Hoffman, Combinatorics of rooted trees and Hopf algebras, Transactions of the American Mathematical Society, vol.355, issue.09, pp.3795-3811, 2003.
DOI : 10.1090/S0002-9947-03-03317-8

M. Livernet, A rigidity theorem for pre-Lie algebras, Journal of Pure and Applied Algebra, vol.207, issue.1, pp.1-18, 2006.
DOI : 10.1016/j.jpaa.2005.10.014

C. Kassel, Quantum groups, Graduate Texts in Mathematics, vol.155, 1995.
DOI : 10.1007/978-1-4612-0783-2
URL : https://hal.archives-ouvertes.fr/hal-00124690

M. Livernet and J. Loday, The Poisson operad as a limit of associative operads, unpublished preprint, 1998.

J. Loday and M. Ronco, Combinatorial Hopf algebras, Clay Math, Proc, vol.11

J. Loday and B. Vallette, Algebraic operads, 2010.

S. and M. Lane, Categories for the working mathematician, Springer Graduate Text in Maths, vol.5, 1971.
DOI : 10.1007/978-1-4612-9839-7

D. Manchon and A. Saïdi, Lois pré-Lie en interaction, Comm. Alg, pp.3662-3680, 2011.

H. Munthe-kaas and W. M. Wright, On the Hopf Algebraic Structure of Lie Group Integrators, Foundations of Computational Mathematics, vol.8, issue.2, pp.227-257, 2008.
DOI : 10.1007/s10208-006-0222-5

M. Markl and E. Remm, Algebras with one operation including Poisson and other Lie-admissible algebras, Journal of Algebra, vol.299, issue.1, pp.171-189, 2006.
DOI : 10.1016/j.jalgebra.2005.09.018

A. Saïdi, On a Pre-Lie Algebra Defined by Insertion of Rooted Trees, Letters in Mathematical Physics, vol.355, issue.2, pp.181-196, 2010.
DOI : 10.1007/s11005-010-0377-5