Geometry of currents, intersection theory and dynamics of horizontal-like maps

DOI10.5802/aif.2188zbMath1089.37036arXivmath/0409272OpenAlexW2154379012MaRDI QIDQ2488757

Tien-Cuong Dinh, Nessim Sibony

Publication date: 15 May 2006

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0409272

zbMATH Keywords

mixingtopological entropyequilibrium measureGreen currentsextremality propertieshorizontal-like mappingsintersection of currents

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Topological entropy (37B40) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Currents (32U40)

Related Items (18)

Attracting currents and equilibrium measures for quasi-attractors of \(\mathbb {P}^k\) ⋮ Attracting current and equilibrium measure for attractors on \(\mathbb P^k\) ⋮ Super-potentials of positive closed currents, intersection theory and dynamics ⋮ Misiurewicz parameters and dynamical stability of polynomial-like maps of large topological degree ⋮ Hyperbolicity and Bifurcations in holomorphic families of polynomial skew products ⋮ Every complex Hénon map is exponentially mixing of all orders and satisfies the CLT ⋮ Dynamical compactifications of \(\mathbb{C}^2\) ⋮ The Mandelbrot set is the shadow of a Julia set ⋮ Upper bound for the topological entropy of a meromorphic correspondence ⋮ On the work of Sarig on countable Markov chains and thermodynamic formalism ⋮ Hyperbolic measure of maximal entropy for generic rational maps of \(\mathbb P^k\) ⋮ Weak convergence of currents ⋮ Dynamics of horizontal-like maps in higher dimension ⋮ Super-potentials for currents on compact Kähler manifolds and dynamics of automorphisms ⋮ Analytic reparametrization of semi-algebraic sets ⋮ Newhouse phenomenon for automorphisms of low degree in \(\mathbb{C}^3\) ⋮ Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k) ⋮ Dynamics of fibered endomorphisms of CP(k)

Cites Work

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