Hyperbolic measure of maximal entropy for generic rational maps of
- [1] U. P. J. V. LAMFA - UMR 7352 33, rue Saint-Leu 80039 Amiens (France)
Annales de l’institut Fourier (2014)
- Volume: 64, Issue: 2, page 645-680
- ISSN: 0373-0956
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top- Eric Bedford, Jeffrey Diller, Energy and invariant measures for birational surface maps, Duke Math. J. 128 (2005), 331-368 Zbl1076.37031MR2140266
- Eric Bedford, John Smillie, Polynomial diffeomorphisms of . III. Ergodicity, exponents and entropy of the equilibrium measure, Math. Ann. 294 (1992), 395-420 Zbl0765.58013MR1188127
- Xavier Buff, Courants dynamiques pluripolaires, Ann. Fac. Sci. Toulouse Math. (6) 20 (2011), 203-214 Zbl1234.37037MR2830397
- Henry De Thélin, Sur les exposants de Lyapounov des applications méromorphes, Invent. Math. 172 (2008), 89-116 Zbl1139.37037MR2385668
- Henry De Thélin, Gabriel Vigny, Entropy of meromorphic maps and dynamics of birational maps, Mém. Soc. Math. Fr. (N.S.) (2010) Zbl1214.37004
- J.-P. Demailly, Complex analytic and differential geometry, (1997)
- Jeffrey Diller, Romain Dujardin, Vincent Guedj, Dynamics of meromorphic maps with small topological degree III: geometric currents and ergodic theory, Ann. Sci. Éc. Norm. Supér. (4) 43 (2010), 235-278 Zbl1197.37059MR2662665
- Jeffrey Diller, Romain Dujardin, Vincent Guedj, Dynamics of meromorphic mappings with small topological degree II: Energy and invariant measure, Comment. Math. Helv. 86 (2011), 277-316 Zbl1297.37022MR2775130
- Jeffrey Diller, Vincent Guedj, Regularity of dynamical Green’s functions, Trans. Amer. Math. Soc. 361 (2009), 4783-4805 Zbl1172.32004MR2506427
- Tien-Cuong Dinh, Viêt-Anh Nguyên, Nessim Sibony, Dynamics of horizontal-like maps in higher dimension, Adv. Math. 219 (2008), 1689-1721 Zbl1149.37025MR2458151
- Tien-Cuong Dinh, Nessim Sibony, Dynamique des applications d’allure polynomiale, J. Math. Pures Appl. (9) 82 (2003), 367-423 Zbl1033.37023MR1992375
- Tien-Cuong Dinh, Nessim Sibony, Dynamics of regular birational maps in , J. Funct. Anal. 222 (2005), 202-216 Zbl1067.37055MR2129771
- Tien-Cuong Dinh, Nessim Sibony, Une borne supérieure pour l’entropie topologique d’une application rationnelle, Ann. of Math. (2) 161 (2005), 1637-1644 Zbl1084.54013MR2180409
- Tien-Cuong Dinh, Nessim Sibony, Distribution des valeurs de transformations méromorphes et applications, Comment. Math. Helv. 81 (2006), 221-258 Zbl1094.32005MR2208805
- Tien-Cuong Dinh, Nessim Sibony, Geometry of currents, intersection theory and dynamics of horizontal-like maps, Ann. Inst. Fourier (Grenoble) 56 (2006), 423-457 Zbl1089.37036MR2226022
- Tien-Cuong Dinh, Nessim Sibony, Pull-back currents by holomorphic maps, Manuscripta Math. 123 (2007), 357-371 Zbl1128.32020MR2314090
- Tien-Cuong Dinh, Nessim Sibony, Super-potentials of positive closed currents, intersection theory and dynamics, Acta Math. 203 (2009), 1-82 Zbl1227.32024MR2545825
- Tien-Cuong Dinh, Nessim Sibony, Super-potentials for currents on compact Kähler manifolds and dynamics of automorphisms, J. Algebraic Geom. 19 (2010), 473-529 Zbl1202.32033MR2629598
- Romain Dujardin, Hénon-like mappings in , Amer. J. Math. 126 (2004), 439-472 Zbl1064.37035MR2045508
- Romain Dujardin, Laminar currents and birational dynamics, Duke Math. J. 131 (2006), 219-247 Zbl1099.37037MR2219241
- Christophe Dupont, Large entropy measures for endomorphisms of , Israel J. Math. 192 (2012), 505-533 Zbl1316.37026MR3009733
- Herbert Federer, Geometric measure theory, (1969), Springer-Verlag New York Inc., New York Zbl0176.00801MR257325
- M. Gromov, Convex sets and Kähler manifolds, Advances in differential geometry and topology (1990), 1-38, World Sci. Publ., Teaneck, NJ Zbl0770.53042MR1095529
- Mikhaïl Gromov, On the entropy of holomorphic maps, Enseign. Math. (2) 49 (2003), 217-235 Zbl1080.37051MR2026895
- Vincent Guedj, Entropie topologique des applications méromorphes, Ergodic Theory Dynam. Systems 25 (2005), 1847-1855 Zbl1087.37015MR2183297
- Vincent Guedj, Ergodic properties of rational mappings with large topological degree, Ann. of Math. (2) 161 (2005), 1589-1607 Zbl1088.37020MR2179389
- Yuri Kifer, Pei-Dong Liu, Random dynamics, Handbook of dynamical systems. Vol. 1B (2006), 379-499, Elsevier B. V., Amsterdam Zbl1130.37301MR2186245
- François Ledrappier, Peter Walters, A relativised variational principle for continuous transformations, J. London Math. Soc. (2) 16 (1977), 568-576 Zbl0388.28020MR476995
- Alexander Russakovskii, Bernard Shiffman, Value distribution for sequences of rational mappings and complex dynamics, Indiana Univ. Math. J. 46 (1997), 897-932 Zbl0901.58023MR1488341