ON POLYNOMIAL AUTOMORPHISM IDENTITY SETS AND IDENTITY POLYNOMIALS

2001 ◽  
Vol 29 (1) ◽  
pp. 319-331
Author(s):  
Wang Mingsheng ◽  
Liu Zhuojun
Keyword(s):  
Polynomial Automorphism

scholarly journals Co-tame polynomial automorphisms

2019 ◽  
Vol 29 (05) ◽  
pp. 803-825 ◽  
Author(s):  
Eric Edo ◽  
Drew Lewis
Keyword(s):  
Characteristic Zero ◽  
Independent Interest ◽  
Technical Tool ◽  
Polynomial Automorphism ◽  
Polynomial Automorphisms ◽  
Negative Results ◽  
Dimension Formula ◽  
Positive Results ◽  
Main Technical Tool

A polynomial automorphism of [Formula: see text] over a field of characteristic zero is called co-tame if, together with the affine subgroup, it generates the entire tame subgroup. We prove some new classes of automorphisms of [Formula: see text], including nonaffine [Formula: see text]-triangular automorphisms, are co-tame. Of particular interest, if [Formula: see text], we show that the statement “Every [Formula: see text]-triangular automorphism is either affine or co-tame” is true if and only if [Formula: see text]; this improves upon positive results of Bodnarchuk (for [Formula: see text], in any dimension [Formula: see text]) and negative results of the authors (for [Formula: see text], [Formula: see text]). The main technical tool we introduce is a class of maps we term translation degenerate automorphisms; we show that all of these are either affine or co-tame, a result that may be of independent interest in the further study of co-tame automorphisms.

Equivariant Polynomial Automorphisms Of Θ-Representations

1998 ◽  
Vol 50 (2) ◽  
pp. 378-400
Author(s):  
Alexandre Kurth
Keyword(s):  
Polynomial Automorphism ◽  
Polynomial Automorphisms

AbstractWe show that every equivariant polynomial automorphism of a Θ- representation and of the reduction of an irreducible Θ-representation is a multiple of the identity.

scholarly journals Extensions of Hénon maps to the closed 4-ball

2000 ◽  
Vol 20 (5) ◽  
pp. 1319-1334
Author(s):  
GREGERY T. BUZZARD
Keyword(s):  
Polynomial Automorphism ◽  
Henon Maps ◽  
Hénon Maps

Any polynomial automorphism of $\mathbb{C}^2$ with nontrivial dynamics is conjugate to a diffeomorphism of the 4-ball such that this diffeomorphism extends to a diffeomorphism of the closed 4-ball. Moreover, the conjugating map is a smooth bijection of $\mathbb{C}^2$ to itself. On the sphere at infinity, the extension has an attracting and a repelling solenoid, and the dynamics near these invariant solenoids are described by conjugation to a model solenoidal map.

Exponential mixing property for Hénon–Sibony maps of

2021 ◽  
pp. 1-13
Author(s):  
HAO WU
Keyword(s):  
Equilibrium Measure ◽  
Polynomial Automorphism ◽  
Exponential Mixing ◽  
Mixing Property

Abstract Let f be a Hénon–Sibony map, also known as a regular polynomial automorphism of $\mathbb {C}^k$ , and let $\mu $ be the equilibrium measure of f. In this paper we prove that $\mu $ is exponentially mixing for plurisubharmonic observables.

scholarly journals The profinite polynomial automorphism group

2015 ◽  
Vol 219 (10) ◽  
pp. 4708-4727 ◽  
Author(s):  
Stefan Maubach ◽  
Abdul Rauf
Keyword(s):  
Automorphism Group ◽  
Polynomial Automorphism

scholarly journals Normal subgroup generated by a plane polynomial automorphism

2010 ◽  
Vol 15 (3) ◽  
pp. 577-610 ◽  
Author(s):  
Jean-Philippe Furter ◽  
Stéphane Lamy
Keyword(s):  
Normal Subgroup ◽  
Polynomial Automorphism

scholarly journals Value distribution of derivatives in polynomial dynamics

2021 ◽  
pp. 1-27
Author(s):  
YÛSUKE OKUYAMA ◽  
GABRIEL VIGNY
Keyword(s):  
Potential Theory ◽  
Number Field ◽  
Julia Set ◽  
Projective Line ◽  
Dirac Measure ◽  
Polynomial Automorphism ◽  
Analytic Sets ◽  
Polynomial Dynamics ◽  
Effective Divisors ◽  
Derivatives Of

Abstract For every $m\in \mathbb {N}$ , we establish the equidistribution of the sequence of the averaged pullbacks of a Dirac measure at any given value in $\mathbb {C}\setminus \{0\}$ under the $m$ th order derivatives of the iterates of a polynomials $f\in \mathbb {C}[z]$ of degree $d>1$ towards the harmonic measure of the filled-in Julia set of f with pole at $\infty $ . We also establish non-archimedean and arithmetic counterparts using the potential theory on the Berkovich projective line and the adelic equidistribution theory over a number field k for a sequence of effective divisors on $\mathbb {P}^1(\overline {k})$ having small diagonals and small heights. We show a similar result on the equidistribution of the analytic sets where the derivative of each iterate of a Hénon-type polynomial automorphism of $\mathbb {C}^2$ has a given eigenvalue.

Sign in / Sign up

Export Citation Format

Share Document