Renormalization, isogenies and rational symmetries of differential equations

Alin Bostan (1) , Salah Boukraa (2) , Samy Hassani (3) , Jean-Marie Maillard (4) , Jacques-Arthur Weil (5) , Nadjah Zenine (3) , Nina Abarenkova (6)

1 ALGORITHMS - Algorithms
2 UB1 - Université Saâd Dahlab Blida 1
3 CRNA - Centre de Recherche Nucléaire d'Alger
4 LPTL - Laboratoire de Physique Théorique des Liquides
5 XLIM-MATHIS - Mathématiques & Sécurité de l'information
6 SMI | RAS - Steklov Mathematical Institute [Moscow]

We give an example of infinite order rational transformation that leaves a linear differential equation covariant. This example can be seen as a non-trivial but still simple illustration of an exact representation of the renormalization group.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Physique Numérique [physics.comp-ph]

Alin Bostan, Salah Boukraa, Samy Hassani, Jean-Marie Maillard, Jacques-Arthur Weil, et al.. Renormalization, isogenies and rational symmetries of differential equations. 2010. ⟨hal-00780425⟩