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Lyapunov exponent and the distribution of the periodic points of an endomorphism of \(\mathbb {CP}^ k\). (Exposants de Liapounoff et distribution des points périodiques d’un endomorphisme de \(\mathbb {CP}^ k\).) (French) Zbl 1144.37436

MSC:
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables
37A25 Ergodicity, mixing, rates of mixing
32V35 Finite-type conditions on CR manifolds
32V15 CR manifolds as boundaries of domains
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[1] Alexander, H. J. &Taylor, B. A., Comparison of two capacities inC n .Math. Z., 186 (1984), 407–417. · Zbl 0576.32029 · doi:10.1007/BF01174894
[2] Bedford, E., Lyubich, M. Yu. &Smillie, J., Distribution of periodic points of polynomial diffeomorphisms ofC 2.Invent. Math., 114 (1993), 272–288. · Zbl 0799.58039 · doi:10.1007/BF01232671
[3] Briend, J.-Y., Exposants de Liapounoff et points périodiques d’endomorphismes holomorphes deCP k . Thèse de doctorat de l’université Paul Sabatier, Toulouse, 1997.
[4] Brolin, H., Invariant sets under iteration of rational functions.Ark. Mat., 6 (1965), 103–144. · Zbl 0127.03401 · doi:10.1007/BF02591353
[5] Cornfeld, I. P., Fomin, S. V. &Sinai, Ya. G.,Ergodic Theory. Grundlehren Math. Wiss., 245. Springer-Verlag, New York-Berlin, 1982.
[6] Fornæss, J. E. &Sibony, N., Complex dynamics in higher dimensions, dansComplex Potential Theory (Montreal, PQ, 1993), p. 131–186. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 439. Kluwer, Dordrecht, 1994. · Zbl 0811.32019
[7] –, Oka’s inequality for currents and applications.Math. Ann., 301 (1995), 399–415. · Zbl 0832.32010 · doi:10.1007/BF01446636
[8] Freire, A., Lopes, A. &Mañé, R., An invariant measure for rational maps.Bol. Soc. Brasil. Mat., 14 (1983), 45–62. · Zbl 0568.58027 · doi:10.1007/BF02584744
[9] Hubbard, J. H. &Papadopol, P., Superattractive fixed points inC n .Indiana Univ. Math. J., 43 (1994), 321–365. · Zbl 0858.32023 · doi:10.1512/iumj.1994.43.43014
[10] Klimek, M.,Pluripotential Theory. London Math. Soc. Monographs (N.S.), 6. Oxford Univ. Press, New York, 1991.
[11] Lyubich, M. Yu., Entropy properties of rational endomorphisms of the Riemann sphere.Ergodic Theory Dynamical Systems, 3 (1983), 351–385. · Zbl 0537.58035
[12] Pollicott, M.,Lectures on Ergodic theory and Pesin Theory on Compact Manifolds. London Math. Soc. Lecture Note Ser., 180. Cambridge Univ. Press, Cambridge, 1993. · Zbl 0772.58001
[13] Ruelle, D., An inequality for the entropy of differentiable maps.Bol. Soc. Brasil. Mat., 9 (1978), 83–87. · Zbl 0432.58013 · doi:10.1007/BF02584795
[14] Tortrat, P., Aspects potentialistes de l’itération des polynômes, dansSéminaire de théorie du potentiel, Paris, no 8, p. 195–209. Lecture Notes in Math., 1235. Springer-Verlag, Berlin, 1987.
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