Characteristic curves and the exponentiation in the Riordan Lie group: A connection through examples

Abstract

We point out how to use the classical characteristic method, that is used to solve quasilinear PDE's, to obtain the matrix exponential of some lower triangle infinite matrices. We use the Lie Fréchet structure of the Riordan group described in [4]. After that, we describe some linear dynamical systems in with a concrete involution being a symmetry or a time-reversal symmetry for them. We take this opportunity to assign some dynamical properties to Pascal's triangle.