Centralisateurs dans le groupe de Jonqui\`eres
Dominique Cerveau, Julie D\'eserti

TL;DR
This paper provides a criterion for linear degree growth of certain birational maps of the complex projective plane fixing a rational fibration and computes their centralizers, addressing classical problems in difference equations.
Contribution
It introduces a new criterion for analyzing degree growth and explicitly computes the centralizer of birational maps preserving rational fibrations.
Findings
Criterion for linear degree growth of birational maps
Explicit description of centralizers of such maps
Connection to classical difference equations problems
Abstract
We give a criterion to determine when the degree growth of a birational map of the complex projective plane which fixes (the action on the basis of the fibration is trivial) a rational fibration is linear up to conjugacy. We also compute the centraliser of such maps. It allows us to describe the centraliser of the birational maps of the complex projective plane which preserve a rational fibration (the action on the basis of the fibration being not necessarily trivial); this question is related to some classical problems of difference equations.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Advanced Topics in Algebra
