Title :

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

Author(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]

English keyword(s) :

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

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

ANR Project :

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