Propriétés ergodiques des applications rationnelles
By Vincent Guedj. 2006
60 citations recorded by the source corpus.
This is a survey article with focus on the following problem. Given $f:X \to X$ a meromorphic endomorphism of some compact Kahler manifold $X$, construct and study - under natural numerical conditions - a canonical invariant probability measure with remarkable ergodic properties (mixing, hyperbolicity, maximal entropy, etc).
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/8613c52874304143b81af6d5ec5a80228ad6cf8a
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Dynamics of automorphisms on projective complex manifolds (2008, methodology): “p from the dynamics on just three types of projective complex manifolds: complex tori, weak Calabi-Yau manifolds and rationally connected manifolds. As a by-product, we confirm the conjecture of Guedj [20] for automorphisms on 3-dimensional projective manifolds, and also determine π1(X). 1. Introduct”
- Dynamics of automorphisms of compact complex surfaces (2014, background): “We tried as much as possible to focus on topics which are not covered by other recent surveys on holomorphic dynamics in several complex variables; we recommend [115], [38], [78], [5], and [58], for complementary material.”
- Building blocks of étale endomorphisms of complex projective manifolds (2009, background): “[13, 26 ]). The kth dynamical degree dk(f ) equals the spectral radius of”
- Normal subgroups in the Cremona group (2010, background): “Transporting this picture in N(1)(X), we obtain: The dynamical degree of g is equal to the dynamical degree of ĝ (see [34], for more general results), the plane Vĝ surjects onto Vg, the image of [F ] is an ample class [D ′] contained in Vg ∩ N(1)(X), and g∗ is the identity on V ⊥ g .”
- Comparison of dynamical degrees for semi-conjugate meromorphic maps (2009, result): “Note that the same result was proved for compact Kähler surfaces by Cantat in [3] and Guedj in [11], and for holomorphic maps on compact Kähler manifolds by Nakayama and Zhang in [14, 21].”
- Open problems in pluripotential theory (2015, background): “, zn), then the answer is positive (see [27]); • if e is Hölder continuous, in particular if φ has analytic singularities, then the answer is positive (see [28,29]); • if φ is bounded from below by γ log ‖z‖ − C, the answer is positive [30]; • when φ is invariant under a rational mapping, the answer”