2007/07/23 by Joost Berson, Berson, Joost, Arno van den Essen +4
Engineering · Mathematics · Physics and Astronomy · #13B25 #13F05 (Secondary) #14R10 (Primary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Control and Dynamics of Mobile Robots #FOS: Mathematics #Quantum chaos and dynamical systems #math.AC #math.AG #msc:13B25 #msc:13F05 #msc:14R10
paper · pdf · doi:10.48550/arxiv.0707.3151
18 pages
openalex publication_date 2007/07/23 · arxiv created 2012/04/19 · arxiv updated 2012/04/20 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
In this paper it is established that all two-dimensional polynomial automorphisms over a regular ring R are stably tame. In the case R is a Dedekind Q-algebra, some stronger results are obtained. A key element in the proof is a theorem which yields the following corollary: Over an Artinian ring A all two-dimensional polynomial automorphisms having Jacobian determinant one are stably tame, and are tame if A is a Q-algebra. Another crucial ingredient, of interest in itself, is that stable tameness is a local property: If an automorphism is locally tame, then it is stably tame.