Propriétés ergodiques des applications rationnelles

Abstract

This is a survey article with focus on the following problem. Given $f:X\to X$ a meromorphic endomorphism of some compact Kähler manifold $X$, construct and study - under natural numerical conditions - a canonical invariant probability measure with remarkable ergodic properties (mixing, hyperbolicity, maximal entropy, etc).

survey, 130p, in french

References in corpus (3)

• Henon mappings in the complex domain II: projective and inductive limits of polynomials
• Monge-Ampère operators on compact Kähler manifolds
• Value distribution of meromorphic transforms and applications

Cited by in corpus (14)

• Normal subgroups in the Cremona group (long version)
• Theorie ergodique des fractions rationnelles sur un corps ultrametrique
• Super-potentials for currents on compact Kaehler manifolds and dynamics of automorphisms
• Dynamics of automorphisms on projective complex manifolds
• Dynamics of Automorphisms of Compact Complex Manifolds
• Holomorphic actions of higher rank lattices in dimension three
• Dynamics of (Pseudo) Automorphisms of 3-space: Periodicity versus positive entropy
• Distribution of points with prescribed derivative in polynomial dynamics
• Cohomologically hyperbolic endomorphisms of complex manifolds
• Comparison of dynamical degrees for semi-conjugate meromorphic maps
• Pull-back of currents by meromorphic maps
• Some problems of arithmetic origin in rational dynamics
• Invertible dynamics on blow-ups of P^k
• Distribution of rational maps with a preperiodic critical point