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On the Lyapunov exponents of meromorphic maps. (Sur les exposants de Lyapounov des applications méromorphes.) (French) Zbl 1139.37037
Author’s summary: Let \(f\) be a dominating meromorphic self-map of a compact Kähler manifold. We give an inequality for the Lyapounov exponents of some ergodic measures of \(f\) using the metric entropy and the dynamical degrees of \(f\). We deduce the hyperbolicity of some measures.

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
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37F50 Small divisors, rotation domains and linearization in holomorphic dynamics
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
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