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SUR L’ÉTUDE DE L’ENTROPIE DES APPLICATIONS MÉROMORPHES

Part of: Holomorphic mappings and correspondences

Published online by Cambridge University Press:  02 November 2017

Henry de Thélin
Henry de Thélin*
Affiliation:
Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), F-93430, Villetaneuse, France ([email protected])
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Abstract

Nous construisons un espace adapté à l’étude de l’entropie des applications méromorphes en utilisant des limites projectives. Nous en déduisons un principe variationnel pour ces applications.

We construct a space which is useful in order to study the entropy of meromorphic maps by using projective limits. We deduce a variational principle for meromorphic maps.

Keywords

dynamique complexeentropie

MSC classification

Primary: 32H50: Iteration problems
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 1 , January 2020 , pp. 1 - 19
Copyright
© Cambridge University Press 2017 

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References

Références

Blanchard, A., Sur les variétés analytiques complexes, Ann. Sci. Éc. Norm. Supér. 73 (1956), 157–202.Google Scholar
Boucksom, S., Favre, C. et Jonsson, M., Degree growth of meromorphic surface maps, Duke Math. J. 141 (2008), 519–538.Google Scholar
Cantat, S., Sur les groupes de transformations birationnelles des surfaces, Ann. of Math. (2) 174 (2011), 299–340.Google Scholar
Dang, N.-B., Degrees of iterates of rational maps on normal projective varieties, preprint, 2017, https://arxiv.org/abs/1701.07760.Google Scholar
De Thélin, H., Sur les exposants de Lyapounov des applications méromorphes, Invent. Math. 172 (2008), 89–116.Google Scholar
De Thélin, H. et Vigny, G., Entropy of meromorphic maps and dynamics of birational maps, Mém. Soc. Math. Fr. 122 (2010).Google Scholar
Dinh, T.-C. et Sibony, N., Regularization of currents and entropy, Ann. Sci. Éc. Norm. Supér. 37 (2004), 959–971.Google Scholar
Dinh, T.-C. et Sibony, N., Une borne supérieure pour l’entropie topologique d’une application rationnelle, Ann. of Math. (2) 161 (2005), 1637–1644.Google Scholar
Gromov, M., On the entropy of holomorphic maps, Enseign. Math. 49 (2003), 217–235.Google Scholar
Guedj, V., Entropie topologique des applications méromorphes, Ergod. Th. & Dynam. Sys. 25 (2005), 1847–1855.Google Scholar
Hironaka, H., Desingularization of complex-analytic varieties, Actes Congrès Intern. Math., Tome 2 (1970), 627–631.Google Scholar
Hubbard, J. H. et Papadopol, P., Newton’s method applied to two quadratic equations in ℂ2 viewed as a global dynamical system, Mem. Amer. Math. Soc. 191 (2008), 891.Google Scholar
Katok, A. et Hasselblatt, B., Introduction to the Modern Theory of Dynamical Systems, Encyclopedia of Mathematics and its Applications, Volume 54 (Cambridge University Press, 1995).Google Scholar
Russakovskii, A. et Shiffman, B., Value distribution for sequences of rational mappings and complex dynamics, Indiana Univ. Math. J. 46 (1997), 897–932.Google Scholar
Sibony, N., Dynamique des applications rationnelles de ℙ k , Panor. Synthèses 8 (1999), 97–185.Google Scholar
Truong, T.-T., (Relative) dynamical degrees of rational maps over an algebraic closed field, preprint, 2015, https://arxiv.org/pdf/1501.01523.pdf.Google Scholar
Ye, X., Topological entropy of the induced maps of the inverse limits with bonding maps, Topology Appl. 67 (1995), 113–118.Google Scholar