Logarithmic derivatives and generalized Dynkin operators

Frederic Menous (1) , Frédéric Patras (2)

1 Département de Mathématiques-Université de Paris XI
2 JAD - Laboratoire Jean Alexandre Dieudonné

Motivated by a recent surge of interest for Dynkin operators in mathematical physics and by problems in the combinatorial theory of dynamical systems, we propose here a systematic study of logarithmic derivatives in various contexts. In particular, we introduce and investigate generalizations of the Dynkin operator for which we obtain Magnus-type formulas.

Mots clés: Free Lie algebras; Logarithmic derivative; Dynkin operator

Domaines: Systèmes dynamiques [math.DS]; Combinatoire [math.CO]; Anneaux et algèbres [math.RA]

Frederic Menous, Frédéric Patras. Logarithmic derivatives and generalized Dynkin operators. Journal of Algebraic Combinatorics, 2013, 38 (4), pp.901-913. ⟨10.1007/s10801-013-0431-3⟩. ⟨hal-00710867⟩