Pseudo-automorphisms with no invariant foliation

2013/09/14 by Eric Bedford, Serge Cantat, Bedford, Eric +3
Mathematics · #14E07 #32H50 #37F10 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS #msc:14E07 #msc:32H50 #msc:37F10

paper · pdf · doi:10.48550/arxiv.1309.3695

openalex publication_date 2013/09/14 · arxiv created 2013/09/26 · arxiv updated 2013/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct an example of a birational transformation of a rational threefold for which the first and second dynamical degrees coincide and are >1, but which does not preserve any holomorphic (singular) foliation. In particular, this provides a negative answer to a question of Guedj. On our way, we develop several techniques to study foliations which are invariant under birational transformations.

Citations

• Explicit Examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy
• Pseudoautomorphisms with invariant elliptic curves
• Dynamics of (Pseudo) Automorphisms of 3-space: Periodicity versus positive entropy
• On automorphisms of blowups of ℙ³
• Salem numbers in dynamics of Kähler threefolds and complex tori

Related

• Examples of Rational Maps of CP² with Equal Dynamical Degrees and No\n Invariant Foliation
• Cycle class maps and birational invariants
• Regularizations of positive entropy pseudo-automorphisms
• Birational Geometry of Special Quotient Foliations and Chazy's Equations
• Piecewise morphisms of birational foliated varieties