Very little is currently known about the dynamics of non-polynomial entire maps in several complex variables. The family of transcendental Henon maps offers the potential of combining ideas from transcendental dynamics in one variable and the dynamics of polynomial Henon maps in two. Here we show that these maps all have infinite topological and measure theoretic entropy. The proof also implies the existence of infinitely many periodic orbits of any order greater than two.

Arosio, L., Benini, A., Fornaess, J., Peters, H. (2021). Dynamics of transcendental Henon maps III: infinite entropy. JOURNAL OF MODERN DYNAMICS, 17, 465-479 [10.3934/jmd.2021016].

Dynamics of transcendental Henon maps III: infinite entropy

Arosio, L;
2021-01-01

Abstract

Very little is currently known about the dynamics of non-polynomial entire maps in several complex variables. The family of transcendental Henon maps offers the potential of combining ideas from transcendental dynamics in one variable and the dynamics of polynomial Henon maps in two. Here we show that these maps all have infinite topological and measure theoretic entropy. The proof also implies the existence of infinitely many periodic orbits of any order greater than two.
2021
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Holomorphic dynamics in several complex variables
complex Henon maps
transcendental Henon maps
automorphisms of C-2
transcendental dynamics
entropy of transcendental maps
Arosio, L., Benini, A., Fornaess, J., Peters, H. (2021). Dynamics of transcendental Henon maps III: infinite entropy. JOURNAL OF MODERN DYNAMICS, 17, 465-479 [10.3934/jmd.2021016].
Arosio, L; Benini, A; Fornaess, J; Peters, H
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/286055
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