M. F. Atiyah and R. Bott, A Lefschetz fixed point formula for elliptic complexes, II. Applications. Ann. of Math, vol.88, issue.2, pp.451-491, 1968.

W. P. Barth, K. Hulek, C. A. Peters, and A. Van-de-ven, Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol.4, 2004.

E. Bedford and K. Kim, Periodicities in linear fractional recurrences: degree growth of birational surface maps, Michigan Math. J, vol.54, issue.3, pp.647-670, 2006.

E. Bedford and K. Kim, Continuous families of rational surface automorphisms with positive entropy, Math. Ann, vol.348, issue.3, pp.667-688, 2010.

J. Blanc, On the inertia group of elliptic curves in the Cremona group of the plane, Michigan Math. J, vol.56, issue.2, pp.315-330, 2008.

J. Blanc and J. Déserti, Embeddings of SL(2, Z) into the Cremona group, Transform. Groups, vol.17, issue.1, pp.21-50, 2012.

J. Blanc, Dynamical degrees of (pseudo)-automorphisms fixing cubic hypersurfaces, Indiana Univ. Math. J, vol.62, issue.4, pp.1143-1164, 2013.

S. Bochner and D. Montgomery, Groups on analytic manifolds, Ann. of Math, vol.48, issue.2, pp.659-669, 1947.

M. Brunella, Publicações Matemáticas do IMPA. Instituto de Matemática Pura e Aplicada (IMPA), 2004.

S. Cantat and I. Dolgachev, Rational surfaces with a large group of automorphisms, J. Amer. Math. Soc, vol.25, issue.3, pp.863-905, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00705290

S. Cantat and C. Favre, Symétries birationnelles des surfaces feuilletées, J. Reine Angew. Math, vol.561, pp.199-235, 2003.

S. Cantat, Dynamics of automorphisms of compact complex surfaces, Frontiers in complex dynamics, vol.62, pp.463-514, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00955973

J. Déserti and J. Grivaux, Automorphisms of rational surfaces with positive entropy, Indiana Univ. Math. J, vol.60, issue.5, pp.1589-1622, 2011.

J. Diller, Cremona transformations, surface automorphisms, and plane cubics, Michigan Math. J, vol.60, issue.2, pp.409-440, 2011.

J. Diller, D. Jackson, and A. Sommese, Invariant curves for birational surface maps, Trans. Amer. Math. Soc, vol.359, issue.6, pp.2793-2991, 2007.

A. Douady, Le problème des modules pour les variétés analytiques complexes (d'après Masatake Kuranishi), Séminaire Bourbaki, vol.9, pp.7-13, 1995.

W. Fischer and H. Grauert, Lokal-triviale Familien kompakter komplexer Mannigfaltigkeiten, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II, pp.89-94, 1965.

H. Flenner, Ein Kriterium für die Offenheit der Versalität, Math. Z, vol.178, issue.4, pp.449-473, 1981.

A. Fujiki, Finite automorphism groups of complex tori of dimension two, Publ. Res. Inst. Math. Sci, vol.24, issue.1, pp.1-97, 1988.

W. Fulton and R. Macpherson, A compactification of configuration spaces, Ann. of Math, vol.139, issue.2, pp.183-225, 1994.

M. H. Gizatullin, Rational G-surfaces, Izv. Akad. Nauk SSSR Ser. Mat, vol.44, issue.1, pp.110-144, 1980.

M. H. Gizatullin, The decomposition, inertia and ramification groups in birational geometry, Algebraic geometry and its applications (Yaroslavlc, 1992), vol.25, pp.39-45, 1994.

P. Griffiths and J. Harris, Principles of algebraic geometry, 1994.

J. Grivaux, Parabolic automorphisms of projective surfaces, vol.16, pp.275-298, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01301468

M. Gromov, On the entropy of holomorphic maps, Enseign. Math, vol.49, issue.2, pp.217-235, 2003.

M. Gross, D. Joyce, and D. Huybrechts, Calabi-Yau Manifolds and Related Geometries, 2003.

B. Harbourne, Rational surfaces with infinite automorphism group and no antipluricanonical curve, Proc. Amer. Math. Soc, vol.99, issue.3, pp.409-414, 1987.

B. Harbourne, Anticanonical rational surfaces, Trans. Amer. Math. Soc, vol.349, issue.3, pp.1191-1208, 1997.

J. Harris and I. Morrison, Moduli of curves, Graduate Texts in Mathematics, vol.187, 1998.

R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, issue.52, 1977.

A. Hirschowitz, Symétries des surfaces rationnelles génériques, Math. Ann, vol.281, issue.2, pp.255-261, 1988.

D. Huybrechts, Complex geometry, 2005.

V. A. Iskovskikh and I. R. Shafarevich,

, Algebraic geometry, vol.II, pp.127-262, 1996.

K. Kodaira, Complex manifolds and deformation of complex structures, Classics in Mathematics, 1981.

K. Kodaira and D. C. Spencer, A theorem of completeness for complex analytic fibre spaces, Acta Math, vol.100, pp.281-294, 1958.

M. Kuranishi, On the Locally Complete Families of Complex Analytic Structures, The Annals of Mathematics, vol.75, issue.3, p.536, 1962.

A. L. Neto, Some examples for the Poincaré and Painlevé problems, INFINITESIMAL DEFORMATIONS OF RATIONAL SURFACE AUTOMORPHISMS, vol.35, issue.4, pp.231-266, 2002.

E. Looijenga, Rational surfaces with an anticanonical cycle, Ann. of Math, vol.114, issue.2, pp.267-322, 1981.

C. T. Mcmullen, Dynamics on K3 surfaces: Salem numbers and Siegel disks, J. Reine Angew. Math, vol.545, pp.201-233, 2002.

C. T. Mcmullen, Dynamics on blowups of the projective plane, Publ. Math. Inst. Hautes Études Sci, issue.105, pp.49-89, 2007.

L. Meersseman, Foliated structure of the Kuranishi space and isomorphisms of deformation families of compact complex manifolds, Ann. Sci. Éc. Norm. Supér, vol.44, issue.4, pp.495-525, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00403954

M. Nagata, On rational surfaces. I. Irreducible curves of arithmetic genus 0 or 1, Mem. Coll. Sci. Univ. Kyoto Ser. A Math, vol.32, pp.351-370, 1960.

M. Namba, On deformations of automorphism groups of compact complex manifolds, Tôhoku Math. J, vol.26, issue.2, pp.237-283, 1974.

L. and P. Medina, Degree of the first integral of a pencil in P 2 defined by Lins Neto, Publ. Mat, vol.57, issue.1, pp.123-137, 2013.

D. S. Rim, Equivariant G-structure on versal deformations, Trans. Amer. Math. Soc, vol.257, issue.1, pp.217-226, 1980.

S. Rollenske, The Kuranishi space of complex parallelisable nilmanifolds, J. Eur. Math. Soc. (JEMS), vol.13, issue.3, pp.513-531, 2011.

E. Sernesi, of Grundlehren der Mathematischen Wissenschaften, vol.334

. Springer-verlag, , 2006.

B. Siebert, Counterexample to the equivariance of versal deformations

H. Tokunaga and H. Yoshihara, Degree of irrationality of abelian surfaces, J. Algebra, vol.174, issue.3, pp.1111-1121, 1995.

T. E. Venkata and . Balaji, An introduction to families, deformations and moduli, 2010.

J. J. Wavrik, Obstructions to the existence of a space of moduli, Global Analysis: Papers in Honor of K. Kodaira (PMS-29), pp.403-414, 1969.

J. J. Wavrik, A theorem of completeness for families of compact analytic spaces, Trans. Amer. Math. Soc, vol.163, pp.147-155, 1972.

Y. Yomdin, Volume growth and entropy, Israel J. Math, vol.57, issue.3, pp.285-300, 1987.

H. Yoshihara, Quotients of abelian surfaces, Publ. Res. Inst. Math. Sci, vol.31, issue.1, pp.135-143, 1995.