Groupes commutatifs d'automorphismes d'une variété kählérienne compacte

By T. Dinh, N. Sibony. 2002

106 citations recorded by the source corpus.

Let V be a compact Kahler manifold. Let Gbe a commutative subgroup of Aut(V ) and U the set of elements of zero entropy of G ' . Then U is a group and Gis isomorphic to the direct product G ' ≃ U × G where G is a subgroup of Gsuch that all elements of G \ {id} are of positive entropy. Moreover, G is a free commutative group with rank(G) ≤ dim V − 1. The estimate is sharp. When rank(G) = dim V − 1, U is finite. Rank(G) satisfies other inequalities involving the dimensions of Dolbeault cohomology groups of V.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6fb2e487b17bb2dc23ac779adec1dc92e0aef31c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Green currents for holomorphic automorphisms of compact Kähler manifolds (2004, background): “It is shown in [15] that the map which associates to a holomorphic endomorphism of X its topological entropy has discrete image in [0,+∞[.”
Rigidity of Julia sets for Henon type maps (2013, background): “We refer the readers to [13, 24, 57] for details.”
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).”
Groups acting on manifolds: around the Zimmer program (2008, result): “The proof of the theorem depends primarily on results concerning Aut(M), particularly recent results on holomorphic actions of abelian groups by Dinh and Sibony [46].”
Distributions in algebraic dynamics (2005, unknown): “See Dinh-Sibony’s paper [22] for details.”
Dynamics of automorphisms of compact complex surfaces (2014, unknown): “Then pluri-potential theory can be applied successfully to construct good f -invariant laminar currents and the unique measure of maximal entropy; this measure describes the distribution of periodic points: See [6] and [66], as well as [50, 51, 52].”