On the Lyapunov exponents of meromorphic maps.

DOI10.1007/s00222-007-0095-5zbMath1139.37037arXivmath/0609628OpenAlexW3098743702MaRDI QIDQ2481311

Henry de Thélin

Publication date: 9 April 2008

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0609628

zbMATH Keywords

meromorphic mappingGreen measureiteration problems

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

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Cites Work

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• Ergodic properties of rational mappings with large topological degree
• An upper bound for the topological entropy of a rational mapping
• Prolongement des courants, positifs, fermes de masse finie
• Lyapunov exponent and the distribution of the periodic points of an endomorphism of \(\mathbb {CP}^k\)
• Dimension of the equilibrium measure of holomorphic maps
• Dynamics of regular birational maps in \(\mathbb P^k\)
• On the entropy of holomorphic maps
• Regularization of currents and entropy
• Entropy and volume
• An inequality for the entropy of differentiable maps
• Value distribution for sequences of rational mappings and complex dynamics
• Green currents for holomorphic automorphisms of compact Kähler manifolds
• Entropie topologique des applications méromorphes
• Propriétés métriques des variétés analytiques complexes définies par une équation
• Two characterizations of equilibrium measure of an endomorphism of \(P^k(\mathbb{C})\)

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