Ergodic properties of rational mappings with large topological degree

By Vincent Guedj. 2005

123 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Cell Biology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/679a402deaad77eaba6968498977d4d0807ca6a2

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Citations in the corpus

Une borne supérieure pour l'entropie topologique d'une application rationnelle (2003, background): “Dans le cas de dimension k ≤ 3 et dans le cas des variétés homogènes, les résultats ci-dessus ont été démontrés par Vincent Guedj [12].”
Dynamics of automorphisms on projective complex manifolds (2008, background): “Results like Lemmas 2.20 and 2.23 are not so essentially used by the paper, but are hopefully of independent interest.”
Current trends and open problems in arithmetic dynamics (2018, background): “It was noted by Guedj [103] that the the sequence of dynamical degrees is concave, i.e., there is a k such that δ (1) f ≤ δ (2) f ≤ · · · ≤ δ (k) f and δ (k) f ≥ δ (k+1) f ≥ · · · ≥ δ (N) f .”
Decay of correlations and the central limit theorem for meromorphic maps (2004, unknown): “D”
Suites d’Applications Méromorphes Multivaluées et Courants Laminaires (2005, background): “Si (Fn) est la suite des itérés d’une application méromorphe (multivaluée) f dont le degré topologique est plus grand que les autres degrés dynamiques, E est contenu dans une réunion dénombrable d’ensembles analytiques, voir Lyubich [21], Briend-Duval [4, 3], Guedj [19] et [9, 8, 10].”
Degree growth of meromorphic surface maps (2006, background): “[Fr, G1 , G2, DS]) and controlling it is necessary in order to construct interesting invariant measures and currents (see e.g.”
Green currents for holomorphic automorphisms of compact Kähler manifolds (2004, background): “It is noticed in [ 29 ] that an inequality of Khovanskii-Teissier-Gromov shows that p 7→ log dp is concave, hence the sequence (dp−1/dp)1≤p≤k is increasing [31, 36, 27].”
Intrinsic capacities on compact Kähler manifolds (2004, methodology): “As an illustration, we obtain transparent proofs of Chern-Levine-Nirenberg type inequalities (see example 1.8 and section 2).”
On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties (2012, background): “rt the proof of Theorem 17 with a preliminary result relating (g◦f)∗ and f∗◦g∗. This is essentially shown in [21, Proofof Proposition 1.2(ii)] by an analytic argument; cf. the equation labeled (†) in [21]. We give an algebraic proof. Proposition 19. Let X,Y,Z be smooth projective varieties of the sa”
Distribution des valeurs de transformations méromorphes et applications (2006, background): “Lorsque X est projective, Vincent Guedj [14] a récemment construit pour f la mesure d’équilibre μ.”
Dynamics of meromorphic maps with small topological degree III: geometric currents and ergodic theory (2008, background): “These bounds are optimal and have been conjectured in [ G2 ] (see [dT2] for recent general results in this direction).”
Equidistribution problems of complex dynamics in higher dimension (2016, methodology): “The convergence has been obtained by the authors for z outside a pluripolar set and by Guedj for z outside a countable union of analytic sets, see [28, 53].”