The dynamical Manin-Mumford problem for plane polynomial automorphisms

DOI10.4171/JEMS/743zbMath1392.37111arXiv1405.1377MaRDI QIDQ1676090

Romain Dujardin, Charles Favre

Publication date: 3 November 2017

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.1377

zbMATH Keywords

nonuniform hyperbolicitypolynomial automorphismnon-Archimedean dynamicsarithmetic equidistributiondynamical heightManin-Mumford problem

Mathematics Subject Classification ID

Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05) Arithmetic properties of periodic points (37P35) Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems (37P30)

Related Items (12)

Algebraic dynamics of the lifts of Frobenius ⋮ A rigidity theorem for Hénon maps ⋮ Periodic subvarieties of semiabelian varieties and annihilators of irreducible representations ⋮ Geometric methods in holomorphic dynamics ⋮ Finite orbits for large groups of automorphisms of projective surfaces ⋮ Unlikely intersection problems for restricted lifts of a \(p\)-th power ⋮ A REFORMULATION OF THE DYNAMICAL MANIN–MUMFORD CONJECTURE ⋮ Rigidity theorems for Hénon maps—II ⋮ The dynamical Manin–Mumford conjecture and the dynamical Bogomolov conjecture for endomorphisms of ⋮ Dynamical degrees of automorphisms on abelian varieties ⋮ On the arithmetic dynamics of monomial maps ⋮ When do two rational functions have locally biholomorphic Julia sets?

Cites Work

• Unnamed Item
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• Local and global canonical height functions for affine space regular automorphisms
• Local dynamics of intersections: V. I. Arnold's theorem revisited
• The arithmetic Hodge index theorem for adelic line bundles
• Preperiodic points and unlikely intersections
• Polynomial diffeomorphisms of \(\mathbb{C}^ 2\). IV: The measure of maximal entropy and laminar currents
• Distribution of postcritically finite polynomials
• Big line bundles over arithmetic varieties
• Equidistribution of small points on abelian varieties
• Positivity and discretion of algebraic points of curves
• Complex Hénon mappings in \({\mathbb{C}}^ 2\) and Fatou-Bieberbach domains
• Polynomial diffeomorphisms of \(\mathbb{C}^ 2\). III: Ergodicity, exponents and entropy of the equilibrium measure
• A remark on the Lefschetz fixed point formula for differentiable maps
• Polynomial diffeomorphisms of \(\mathbb{C}^2\). VI: Connectivity of \(J\)
• On the degree of iterates of automorphisms of the affine plane
• Distribution of periodic points of polynomial diffeomorphisms of \(\mathbb{C}^ 2\)
• Equidistribution of small points
• The intersection of laminar currents
• Reversible polynomial automorphisms of the plane: the involutory case
• Polynomial diffeomorphisms of \({\mathbb{C}}^2\). V: Critical points and Lyapunov exponents
• The equidistribution of small points for strongly regular pairs of polynomial maps
• Invariant varieties for polynomial dynamical systems
• Canonical height functions for affine plane automorphisms
• Polynomial diffeomorphisms of \({\mathbb C}^2\): Currents, equilibrium measure and hyperbolicity
• Points entiers sur les surfaces arithmétiques
• Forms and Currents on the Analytification of an Algebraic Variety (After Chambert-Loir and Ducros)
• LOCAL ANALYTIC CONJUGACY OF SEMI-HYPERBOLIC MAPPINGS IN TWO VARIABLES, IN THE NON-ARCHIMEDEAN SETTING
• Towards a Dynamical Manin-Mumford Conjecture
• Heights and measures on analytic spaces. A survey of recent results, and some remarks
• Elliptic isles in families of area-preserving maps
• Dimension, entropy and Lyapunov exponents
• Dynamical properties of plane polynomial automorphisms
• Local heights of subvarieties over non-archimedean fields
• POLARIZED MORPHISMS BETWEEN ABELIAN VARIETIES
• Solution to a non-Archimedean Monge-Ampère equation
• Canonical heights for Hénon maps
• Mesures et équidistribution sur les espaces de Berkovich
• The Tits alternative for \(\text{Aut}[\mathbb C^2\)]

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