Titre :

Monotonicity of dynamical degrees for Hénon-like and polynomial-like maps

Auteur(s) :

Bianchi, Fabrizio [Auteur]
Centre National de la Recherche Scientifique [CNRS]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Dinh, Tien-Cuong [Auteur]
National University of Singapore [NUS]
Rakhimov, Karim [Auteur]
National University of Singapore [NUS]

Mot(s)-clé(s) en anglais :

Horizontal-like maps
Polynomial-like maps
Dynamical degrees
Deformation of currents

Discipline(s) HAL :

Mathématiques [math]/Systèmes dynamiques [math.DS]
Mathématiques [math]/Variables complexes [math.CV]

Résumé en anglais : [en]

We prove that, for every invertible horizontal-like map (i.e., Hénon-like map) in any dimension, the sequence of the dynamical degrees is increasing until that of maximal value, which is the main dynamical degree, and ...
Lire la suite >We prove that, for every invertible horizontal-like map (i.e., Hénon-like map) in any dimension, the sequence of the dynamical degrees is increasing until that of maximal value, which is the main dynamical degree, and decreasing after that. Similarly, for polynomial-like maps in any dimension, the sequence of dynamical degrees is increasing until the last one, which is the topological degree. This is the first time that such a property is proved outside of the algebraic setting. Our proof is based on the construction of a suitable deformation for positive closed currents, which relies on tools from pluripotential theory and the solution of the $d$, $\bar \partial$, and $dd^c$ equations on convex domains.Lire moins >

Langue :

Anglais

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
ULNE
Quantisation, singularités et dynamique holomorphe
Dynamique parabolique, bifurcations et domaines errants

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL