A phenomenon of concentration of genus.

DOI10.1007/s00208-005-0631-9zbMath1076.37037arXivmath/0503260OpenAlexW2005491432MaRDI QIDQ2484084

Henry de Thélin

Publication date: 2 August 2005

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503260

zbMATH Keywords

Green measurelaminar currents

Mathematics Subject Classification ID

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) Hyperbolic and Kobayashi hyperbolic manifolds (32Q45) Currents (32U40)

Related Items (14)

A non-laminar dynamical Green current ⋮ On the regular automorphisms of \(\mathbb{C}^k\). ⋮ Structure of Julia sets for post-critically finite endomorphisms on \(\mathbb{P}^2\) ⋮ Attracting current and equilibrium measure for attractors on \(\mathbb P^k\) ⋮ Upper bound for the topological entropy of a meromorphic correspondence ⋮ Dimension of ergodic measures and currents on ⋮ Fatou directions along the Julia set for endomorphisms of \({\mathbb{CK}}^k\) ⋮ On saddle measures ⋮ On the measures of large entropy on a positive closed current ⋮ Dynamics of post-critically finite maps in higher dimension ⋮ Hyberbolic saddle measures and laminarity for holomorphic endomorphisms of P^2C ⋮ The bifurcation measure has maximal entropy ⋮ Entropy of meromorphic maps acting on analytic sets ⋮ Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k)

Cites Work

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• Polynomial diffeomorphisms of \(\mathbb{C}^ 2\). IV: The measure of maximal entropy and laminar currents
• Laminar currents in \(\mathbb P^2\)
• Brolin's theorem for curves in two complex dimensions.
• The intersection of laminar currents
• On the entropy of holomorphic maps
• Sur la laminarité de certains courants
• Propriétés métriques des variétés analytiques complexes définies par une équation
• Geometry and spectra of compact Riemann surfaces
• Two characterizations of equilibrium measure of an endomorphism of \(P^k(\mathbb{C})\)

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