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Un théorème de semi-continuité pour l’entropie des applications méromorphes

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Résumé

Nous montrons un théorème de semi-continuité supérieure pour l’entropie métrique des applications méromorphes.

Abstract

We prove a theorem of uppersemicontinuity for the metric entropy of meromorphic maps.

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References

  1. De Thélin, H.: Sur les exposants de Lyapounov des applications méromorphes. Invent. Math. 172, 89–116 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. De Thélin, H., Vigny, G.: Entropy of meromorphic maps and dynamics of birational maps. Mém. Soc. Math. Fr. 122 (2010)

  3. Dinh, T.-C., Dupont, C.: Dimension de la mesure d’équilibre d’applications méromorphes. J. Geom. Anal. 14, 613–627 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dinh, T.-C., Sibony, N.: Regularization of currents and entropy. Ann. Ecole Norm. Sup. 37, 959–971 (2004)

    MATH  MathSciNet  Google Scholar 

  5. Dinh, T.-C., Sibony, N.: Une borne supérieure pour l’entropie topologique d’une application rationnelle. Ann. Math. 161, 1637–1644 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dupont, C.: Large entropy measures for endomorphisms of \({\mathbb{C}}{\mathbb{P}}^k\). Isr. J. Math. 192, 505–533 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  7. Froyland, G., Lloyd, S., Quas, A.: Coherent structures and isolated spectrum for Perron-Frobenius cocycles. Ergodic Theory Dynam. Syst. 30, 729–756 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  8. Gromov, M.: On the entropy of holomorphic maps. Enseign. Math. 49, 217–235 (2003)

    MATH  MathSciNet  Google Scholar 

  9. Mañé, R.: A proof of Pesin’s formula. Ergod. Theory Dynam. Syst. 1, 95–102 (1981)

    Article  MATH  Google Scholar 

  10. Mañé, R.: Lyapounov exponents and stable manifolds for compact transformations. Lecture Notes in Math. 1007, 522–577 (1983)

    Article  Google Scholar 

  11. Newhouse, S.E.: Entropy and volume. Ergodic Theory Dynam. Syst. 8, 283–299 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  12. Newhouse, S.E.: Continuity properties of entropy. Ann. Math. 129, 215–235 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  13. Thieullen, P.: Fibrés dynamiques asymptotiquement compacts. Exposants de Lyapounov. Entropie. Dimension. Ann. Inst. H. Poincaré Anal. Non Linéaire 4, 49–97 (1987)

    MATH  MathSciNet  Google Scholar 

  14. Yomdin, Y.: Volume growth and entropy. Isr. J. Math. 57, 285–300 (1987)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), 93430, Villetaneuse, France

    Henry de Thélin

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  1. Henry de Thélin
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Correspondence to Henry de Thélin.

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de Thélin, H. Un théorème de semi-continuité pour l’entropie des applications méromorphes. Math. Ann. 362, 1–23 (2015). https://doi.org/10.1007/s00208-014-1101-z

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  • DOI: https://doi.org/10.1007/s00208-014-1101-z

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