Vigny Gabriel

Je travaille en dynamique complexe à plusieurs variables, en théorie des bifurcations et en dynamique arithmétique à travers l'utilisation de la théorie du pluripotentiel.

Prépublications

1- T. Gauthier, J. Taflin et G. VIgny. Sparsity of postcritically finite maps of Pk and beyond: A complex analytic approach, https://arxiv.org/abs/2305.02246, 2023.

2- T Gauthier, G. Vigny, Gauthier, Julia sets and bifurcation loci. https://arxiv.org/abs/2411.16178 (2024).

Publications

1- G. Vigny. Dirichlet-like space and capacity in complex analysis in several variables. J. Funct. Anal., 252(1):247–277, 2007.

2- G. Vigny. Dynamics semi-conjugated to a subshift for some polynomial mappings in C2 . Publ. Mat., 51(1):201–222, 2007.

3- G. Vigny Lelong-Skoda transform for compact Kähler manifolds and self-intersection inequalities. J. Geom. Anal., 19(2):433–451, 2009.

4- H. De Thélin et G. Vigny. Entropy of meromorphic maps and dynamics of birational maps. Mém. Soc. Math. Fr. (N.S.), 122:vi+98, 2010.

5- G. Vigny. Hyperbolic measure of maximal entropy for generic rational maps of Pk . Ann. Inst. Fourier (Grenoble), 64(2):645–680, 2014.

6- G. Vigny. Exponential decay of correlations for generic regular birational maps of Pk . Math. Ann., 362(3-4):1033–1054, 2015.

7- H. De Thélin et G. Vigny. On the measures of large entropy on a positive closed current. Math. Z., 280(3-4):919–944, 2015.

8- T. Gauthier et G. Vigny. Distribution of postcritically finite polynomials II: Speed of convergence. J. Mod. Dyn., 11:57–98, 2017.

9- T. Gauthier et G. Vigny. Distribution of points with prescribed derivative in polynomial dynamics. Riv. Math. Univ. Parma (N.S.), 8(2), 247–270, 2017.

10- T. Gauthier et G. Vigny. Distribution of postcritically finite polynomials III: Combinatorial continuity. Fund. Math., 244(1):17–48, 2019.

11- M. Astorg, T. Gauthier, N. Mihalache, et G. Vigny. Collet, Eckmann and the bifurcation measure. Invent. Math., 217(3), 749–797, 2019.

12- T. Gauthier, Y. Okuyama et G. Vigny. Hyperbolic components of rational maps: Quantitative equidistribution and counting. Comment. Math. Helv., 94(2), 347–398, 2019.

13- T. Gauthier, Y. Okuyama et G. Vigny. Approximation of non-archimedean Lyapunov exponents and applications over global fields. Trans. Amer. Math. Soc., 373, no. 12, 8963-9011, 2020.

14- H. De Thélin,T. Gauthier et G. Vigny. The bifurcation measure has maximal entropy. Israel J. Math., 235(1), 213–243, 2020.

15- H. De Thélin et G. Vigny. Entropy of meromorphic maps acting on analytic sets. Indiana Univ. Math. Journ. 70, no. 1, 157–178, 2021.

16- Y. Okuyama et G. Vigny. Value distribution of derivatives in polynomial dynamics. Ergodic Theory Dynam. Systems, 41, no. 12, 3780–3806, 2021.

17- H. De Thélin,T. Gauthier et G. Vigny. Parametric Lyapunov exponents. Bull. Lond. Math. Soc., 53, no. 3, 660–672, 2021.

18- T. Gauthier et G. Vigny. The geometric dynamical Northcott property for regular polynomial automorphisms of the affine plane. Bulletin de la SMF, 150(4), 677-698, 2022

19- G. Vigny et D.-V. Vu. Lebesgue points of functions in the complex Sobolev space, Internat. J. Math. 35 (2024), no. 5, Paper No. 2450014, 22 pp.

20 - T. Gauthier et G. Vigny. The Geometric Dynamical Northcott and Bogomolov Properties. https://arxiv.org/abs/1912.07907, preprint 2019. A paraître aux Annales de l'ENS

21 - T. Gauthier et G. Vigny. Complex Dynamics of birational maps of Pk defined over a number field, https://arxiv.org/abs/2303.12585, 2023. A paraître au Jour. Anal. Math. Autres documents

22 - T. Gauthier et G. Vigny. Variation of canonical heights of subvarieties for polarized endomorphisms. https://arxiv.org/abs/2307.11243, 2023. A paraître à JTNB

Autres textes

T. Gauthier et G. Vigny. The Geometric Dynamical Northcott Property in the quadratic family. https://arxiv.org/abs/2307.11245 (Il s'agit d'une version simplifiée de nos travaux dans le cadre de la famille quadratique, non destinée à la publication).

J'ai participé à l'élaboration du recueil de problèmes "Hénon maps: a list of open problems. arXiv:2312.03907" de Julia Hénon de Xénékis, A paraître à Arnold journal of Math.