+. Aadb, ]. N. Abarenkova, J. Ch, S. Boukraa, S. Hassani et al.,

F. Maillard and . Yang, Baxter equations to dynamical zeta functions for birational transformations, Statistical physics on the eve of the 21st century

. Statist and . Mech, World Sci. Publ., River Edge NJ, vol.14, pp.436-490, 1999.

]. N. Aadbm99, J. Abarenkova, S. Chauriac, J. Boukraa, and . Maillard, Growthcomplexity spectrum of some discrete dynamical systems The product on smooth and generalized valuations, Phys. D Amer. J. Math, vol.130, issue.134 2, pp.27-42, 1999.

, MR 3707644 [ADM99] Semyon Alesker, Sean Dar, and Vitali Milman, A remarkable measure preserving diffeomorphism between two convex bodies in R n, J. Differential Geom. Geom. Dedicata, vol.107, issue.74 2, pp.203-240, 1999.

J. Anglès-d-'auriac, J. Maillard, C. M. Vialletaf14-]-semyon-alesker, and J. H. Fu, On the complexity of some birational transformations Integral geometry and valuations, Lectures from the Advanced Course on Integral Geometry and Valuation Theory held at the Centre de Recerca Matemàtica (CRM) MR 3380549 [Ale38] Aleksandr Danilovich Alexandrov, On the theory of mixed volumes of convex bodies III. extension of two theorems of Minkowski on convex polyhedra to arbitrary convex bodies., Mat. Sbornik, pp.3641-3654, 1938.

A. Alesker, Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture, Geometric and Functional Analysis, vol.11, issue.2, pp.244-272, 2001.
DOI : 10.1007/PL00001675

, The multiplicative structure on continuous polynomial valuations

. Funct, Theory of valuations on manifolds : a survey MR 2373020 [Ale11] , A Fourier-type transform on translation-invariant valuations on convex sets, MR 2053598 [Ale07], pp.1-26, 2004.

J. Blanc and S. Cantat, Dynamical degrees of birational transformations of projective surfaces, Journal of the American Mathematical Society, vol.29, issue.2, pp.415-471, 2016.
DOI : 10.1090/jams831

URL : https://hal.archives-ouvertes.fr/hal-00905779

[. Boucksom, C. Tomasso-de-fernex, S. Favre, and . Urbinati, Valuation spaces and multiplier ideals on singular varieties, Recent advances in algebraic geometry, Soc. Lecture Note Ser, vol.417, pp.29-51
URL : https://hal.archives-ouvertes.fr/hal-01708663

N. David and . Bernstein, The number of roots of a system of equations, Funkcional. Anal. i Prilo?en, vol.9, issue.3, pp.1-4, 1975.

A. Bernig, Algebraic integral geometry, Global Differential Geometry, pp.107-145, 2012.

A. Bernig and J. H. Fu, Convolution of convex valuations, Geometriae Dedicata, vol.46, issue.1, pp.153-169, 2006.
DOI : 10.1515/9781400877577

A. Bernig and D. Faifman, Degree growth of meromorphic surface maps, Duke Math Degree growth of meromorphic surface maps The tame automorphism group of an affine quadric threefold acting on a square complex, MR 3451918 [BFJ08a] Sébastien Boucksom, Charles Favre, and Mattias Jonsson MR 2387430 [BFJ08b] Sébastien Boucksom, Charles Favre, and Mattias JonssonBFL14] Cinzia Bisi, Jean-Philippe Furter, and Stéphane Lamy, pp.36-72, 2008.

R. Martin, A. Bridson, and . Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of, Mathematical Sciences], vol.319, p.1744486, 1999.

F. Lo and B. , On the primitivity of birational transformations of irreducible symplectic manifolds, arXiv preprint, 2016.

[. Brenier, Polar factorization and monotone rearrangement of vector-valued functions, Communications on Pure and Applied Mathematics, vol.117, issue.4, pp.375-417, 1991.
DOI : 10.1002/cpa.3160440402

W. Ballmann and J. Swiatkowski, On groups acting on nonpositively curved cubical complexes, Enseign. Math, issue.2 12, pp.45-51, 1999.

D. Chen and I. Coskun, Extremal higher codimension cycles on moduli spaces of curves, Proceedings of the London Mathematical Society, vol.330, issue.1, pp.181-204, 2015.
DOI : 10.1006/jabr.2001.9044

I. Coskun, J. Lesieutre, and J. C. Ottem, Effective cones of cycles on blow-ups of projective space, arXiv preprint 1603, p.4808, 2016.
DOI : 10.2140/ant.2016.10.1983

URL : http://arxiv.org/pdf/1603.04808

A. David, J. B. Cox, H. K. Little, and . Schenck, Toric varieties, Graduate Studies in Mathematics, vol.124, pp.2011-2810322

S. Cantat and K. Oguiso, Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups, American Journal of Mathematics, vol.137, issue.4, pp.1013-1044, 2015.
DOI : 10.1353/ajm.2015.0023

URL : https://hal.archives-ouvertes.fr/hal-00858904

C. Steven-dale, Teissier's problem on inequalities of nef divisors Automorphism groups of positive entropy on projective threefolds, J. Algebra Appl. Trans. Amer. Math. Soc, vol.14, issue.366 3, pp.1621-1638, 2014.

, Degrees of iterates of rational maps on normal projective varieties, 2017.

[. Debarre, Higher-dimensional algebraic geometry, 2001.
DOI : 10.1007/978-1-4757-5406-3

O. Debarre, L. Ein, R. Lazarsfeld, and C. Voisin, Abstract, MR 2862063 [DELV11b] , Pseudoeffective and nef classes on abelian varieties, pp.1793-1818, 2011.
DOI : 10.1007/s00039-009-0036-0

J. Demailly, Analytic methods in algebraic geometry Complex analytic and differential geometry. online book, available at wwwfourier . ujf-grenoble, Surveys of Modern Mathematics, vol.1, 2012.

J. Diller, C. Favre-surfaces, . J. Amer, and . Math, MR 1867314 [Din05] Tien-Cuong Dinh, Suites d'applications méromorphes multivaluées et courants laminaires MR 2152480 [DN11a] Tien-Cuong Dinh and Viêt-Anh Nguyên, Comparison of dynamical degrees for semi-conjugate meromorphic maps Comparison of dynamical degrees for semi-conjugate meromorphic maps, MR 2851870 [DNT12] Tien-Cuong Dinh, Viêt-Anh Nguyên, and Tuyen Trung Truong, On the dynamical degrees of meromorphic maps preserving a fibration, pp.1135-1169, 2001.

T. Dinh, N. Sibony-entropy, and A. Sci, École Norm Regularization of currents and entropy, Annales scientifiques de l'École normale supérieure 37 [DS05a] , Green currents for holomorphic automorphisms of compact Kähler manifolds Une borne supérieure pour l'entropie topologique d'une application rationnelle Une borne supérieure pour l'entropie topologique d'une application rationnelle, With a view toward algebraic geometry. MR 1322960 [FGI + 05, pp.959-971, 1995.

B. Fantechi, L. Göttsche, L. Illusie, S. Kleiman, N. Nitsure et al., Fundamental algebraic geometry : Grothendieck's fga explained, Mathematical Surveys and Monographs, vol.123, 2005.
DOI : 10.1090/surv/123

W. Fulton and J. Harris, Representation theory, Graduate Texts in Mathematics, vol.129, 1991.

C. Favre and M. Jonsson, Ann. of Math, issue.22 1, pp.173-211, 2011.

M. Fulger and B. Lehmann, Kernels of numerical pushforwards, arXiv preprint 1407, 2014.

, Positive cones of dual cycle classes, arXiv preprint 1408, 2014.

J. Friedland and . Milnor, Dynamical properties of plane polynomial automorphisms , Ergodic Theory Dynam, Systems, vol.9, issue.1, pp.67-99, 1989.

J. E. , F. , and N. Sibony, Complex dynamics in higher dimension. II, Modern methods in complex analysis, Ann. of Math. Stud, vol.137, pp.135-182, 1992.

W. Fulton, Introduction to toric varieties The William H. Roever Lectures in Geometry, Annals of Mathematics Studies, vol.131, 1993.

, MR 1644323 [FW12] Charles Favre and Elizabeth Wulcan, Degree growth of monomial maps and Mc- Mullen's polytope algebra, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas, pp.61-493, 1998.

E. García, Fibrés d'intersection, Compositio Math, pp.219-252, 2000.

[. Gil, W. Gubler, P. Jell, K. Kuennemann, and F. Martin, Differentiability of non-archimedean volumes and nonarchimedean monge-amp\ere equations (with an appendix by robert lazarsfeld), arXiv preprint 1608, p.1919, 2016.

[. Gizatullin, G. Rational, . Izv, and . Akad, MR 563788 [Gro87] Misha Gromov, Entropy, homology and semialgebraic geometry, MR 880035 [Gro90] Misha Gromov, Convex sets and Kähler manifolds, Advances in Differential Geometry and Topology, pp.110-144, 1980.

, Algebraic geometry, 1977.

J. Darald and . Hartfiel, Dense sets of diagonalizable matrices, Proc. Amer, pp.1669-1672, 1995.

B. Huber and B. Sturmfels, A polyhedral method for solving sparse polynomial systems Valuations and asymptotic invariants for sequences of ideals, Math. Comp. Ann. Inst. Fourier (Grenoble), vol.64, issue.62 6, pp.1541-1555, 1995.

A. Jong, Smoothness, semi-stability and alterations, Publications Mathématiques de l, IHÉS, 1996.

W. E. Heinrich, . Jung, J. R. Über-ganze-birationale-transformationen-der-ebene, and . Angew, Math, vol.184, pp.161-174, 1942.

A. Georgievich-khovanski?-i, Newton polyhedra, and the genus of complete intersections, Funktsional. Anal. i Prilozhen, vol.12, issue.1, pp.51-61, 1978.

J. Kollár and S. Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, vol.134, 1998.
DOI : 10.1017/CBO9780511662560

[. Kuroda, Weighted multidegrees of polynomial automorphisms over a domain, Journal of the Mathematical Society of Japan, vol.68, issue.1, pp.119-149, 2016.
DOI : 10.2969/jmsj/06810119

. Anatolii-georgievich-kushnirenko and . Polyèdres-de-newton-et-nombres-de-milnor, Invent. Math, vol.32, issue.1, pp.1-31, 1976.

S. Lamy, Combinatorics of the tame automorphism group, arXiv preprint, 2015.

S. Lang and A. , Graduate Texts in Mathematics, vol.211, 2002.

R. Lazarsfeld, Positivity in algebraic geometry. I, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics Classical setting : line bundles and linear series, Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 2004.

S. Lefschetz and N. J. , Algebraic geometry, p.56950, 1953.
DOI : 10.1515/9781400876686

J. Lesieutre, Some constraints on positive entropy automorphisms of smooth threefolds, arXiv preprint, 2015.

J. Lin, Algebraic stability and degree growth of monomial maps, Mathematische Zeitschrift, vol.27, issue.5, pp.293-311, 2012.
DOI : 10.1017/S0143385707000168

S. Lamy and P. Przytycki, Acylindrical hyperbolicity of the threedimensional tame automorphism group, arXiv preprint, 2016.

, Presqu'un immeuble pour le groupe des automorphismes mod\'er\'es, arXiv preprint arXiv :1802, p.481, 2018.

, Presqu'un immeuble pour le groupe des automorphismes mod\'er\'es, arXiv preprint arXiv :1802, p.481, 2018.

S. Lamy and S. Vénéreau, The tame and the wild automorphisms of an affine quadric threefold, Journal of the Mathematical Society of Japan, vol.65, issue.1, pp.299-320, 2013.
DOI : 10.2969/jmsj/06510299

B. Lehmann and J. Xiao, Convexity and Zariski decomposition structure, Geometric and Functional Analysis, vol.76, issue.3, 2015.
DOI : 10.2307/1970376

URL : https://hal.archives-ouvertes.fr/hal-01684170

, Convexity and zariski decomposition structure

, Correspondences between convex geometry and complex geometry, Convexity and Zariski decomposition structure, pp.1135-1189, 2016.

R. J. Mccann, Existence and uniqueness of monotone measure-preserving maps., Duke Math, J, vol.80, issue.2, pp.309-323, 1995.

P. Mcmullen, MR 0448239 BIBLIOGRAPHIE [McM80] , Continuous translation-invariant valuations on the space of compact convex sets, MR 593954 [McM93] , Valuations and dissections, Handbook of convex geometry, pp.113-135, 1977.

J. S. Milne, Lectures on etale cohomology (v2.21), 2013, Available at www.jmilne.org/math

P. Mcmullen and R. Schneider, Valuations on convex bodies, Convexity and its applications, pp.170-247, 1983.

K. Oguiso and T. Truong, Salem numbers in dynamics on Kähler threefolds and complex tori Explicit examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy, Math. Z. J. Math. Sci. Univ. Tokyo, vol.278, issue.22 1, pp.93-117, 2014.

P. Papasoglu, Strongly geodesically automatic groups are hyperbolic, Inventiones Mathematicae, vol.16, issue.1, pp.323-334, 1995.
DOI : 10.1007/BF01884301

D. Popovici, Volume and self-intersection of differences of two nef classes, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01976319

, Sufficient bigness criterion for differences of two nef classes, Math. Ann, vol.364, issue.12, pp.649-655, 2016.

D. Popovici, Sufficient bigness criterion for differences of two nef classes, Mathematische Annalen, vol.23, issue.4, pp.649-655, 2016.
DOI : 10.1090/S0894-0347-2010-00673-X

URL : https://hal.archives-ouvertes.fr/hal-01976325

L. Parapatits and T. Wannerer, On the inverse Klain map, Duke Math, J, vol.162, issue.11, pp.1895-1922, 2013.

A. Russakovskii and B. Shiffman, Value distribution for sequences of rational mappings and complex dynamics, Indiana University Mathematics Journal, vol.46, issue.3, pp.897-932, 1997.
DOI : 10.1512/iumj.1997.46.1441

R. Schneider, Convex bodies : the Brunn-Minkowski theory, p.2014
DOI : 10.1017/CBO9780511526282

Y. Tong and S. , An effective Matsusaka big theorem, Ann. Inst. Fourier (Grenoble), vol.43, issue.5, pp.1387-1405, 1993.

P. Ivan, . Shestakov, U. Ualbai, and . Umirbaev, The nagata automorphism is wild, Proceedings of the National Academy of Sciences, vol.100, issue.22, pp.12561-12563, 2003.

I. Soprunov and A. Zvavitch, Bezout inequality for mixed volumesrelative) dynamical degrees of rational maps over an algebraic closed field, Int. Math. Res. Not. IMRN, issue.23, pp.7230-7252, 2015.

, Relative dynamical degrees of correspondance over a field of arbitrary characteristic, 2016.

T. Truong, Automorphisms of blowups of threefolds being Fano or having Picard number 1, Ergodic Theory Dynam, MR 3693127 [Ure16] Christian Urech, Remarks on the degree growth of birational transformations, arXiv preprint 1606, pp.727-753, 2016.

M. Vaquié and . Valuations, Resolution of singularities (Obergurgl, 1997), Progr. Math, vol.181, pp.539-590, 2000.

C. Voisin, Hodge theory and complex algebraic geometry. I, english ed, Cambridge Studies in Advanced Mathematics, vol.76, 2007.
DOI : 10.1017/cbo9780511615344

D. Wright, THE GENERALIZED AMALGAMATED PRODUCT STRUCTURE OF THE TAME AUTOMORPHISM GROUP IN DIMENSION THREE, Transformation Groups, vol.331, issue.1, pp.291-304, 2015.
DOI : 10.1090/S0002-9947-1992-1038019-2

J. Xiao, In??galit??s de Morse holomorphes transcendantes faibles sur les vari??t??s k??hleriennes, MR 3449182 [Xia17] , Bézout type inequality in convex geometry, pp.1367-1379, 2015.
DOI : 10.5802/aif.2959

D. Zhang, Dynamics of automorphisms on projective complex manifolds, Journal of Differential Geometry, vol.82, issue.3, pp.691-722, 2009.
DOI : 10.4310/jdg/1251122550

URL : https://doi.org/10.4310/jdg/1251122550

, Automorphism groups of positive entropy on minimal projective varieties, Adv. Math, vol.225, issue.5, pp.2332-2340, 2010.