Green currents for holomorphic automorphisms of compact Kähler manifolds

By T. Dinh, N. Sibony. 2004

103 citations recorded by the source corpus.

and some additional regularity properties. Very likely, the currents T will describe the distribution of invariant manifolds of codimension s corresponding to the small est Lyapounov exponents. Let dp denote the dynamical degree of order p of /. It describes the growth under iteration of the volume of p-dimensional manifolds. When d\ > 1, it is natural to introduce first a positive closed (1, l)-current as ifnYoj 7\ := lim ^?-.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d94dc0ae19ab20e06bf7a9123158c4f151bd6958

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Dynamics of automorphisms on projective complex manifolds (2008, methodology): “We refer to Gromov [16], Yomdin [50], Friedland [11], and Dinh - Sibony [9] page 302, for the definition of the i-th dynamical degree di(g) for 1 ≤ i ≤ n = dimX (note that dn(g) = 1 now and set d0(g) = 1) and the actual definition of the topological entropy h(g) which turns out to be log ρ(g) in the”
Dynamics of automorphisms of compact complex surfaces (2014, unknown): “6 (Dinh-Sibony [56], Moncet [106], Ueda [119]).”
A theorem of Tits type for compact Kähler manifolds (2008, background): “We refer to [7], [18], [6], [3] and [4] for the definitions of the i-th dynamical degrees di(g) and the topological entropy h(g) for g ∈ Aut(X).”
Suites d’Applications Méromorphes Multivaluées et Courants Laminaires (2005, background): “Nous renvoyons le lecteur `a [10, 11 ] pour l’´etude de la convergence de cette suite vers des courants invariants ainsi que pour les propri´et´es dynamiques de courants limites (courants de Green).”
Rigidity of Julia sets for Henon type maps (2013, background): “For automorphisms of compact Kähler manifolds see Cantat, de Thélin-Dinh, Dinh-Sibony [10, 18, 26, 30, 33], for the semi-local setting of horizontal-like maps see Dinh-Nguyen-Sibony, Dujardin [23, 27, 34], for non-injective holomorphic maps see the survey [31] and the references therein.”