NORMAL FORMS OF REVERSIBLE DYNAMICAL-SYSTEMS

We consider reversible dynamical systems with a fixed point which is a lso fixed under the reversing involution; we show that applying to suc h a system the canonical Poincare-Dulac procedure reducing a dynamical system to its normal form, we obtain a normal form which is still rev ersible (under the same involution as the original system); conversely , we also show how to obtain ah the reversible systems which are reduc ed to a given reversible form. This allows one to (locally) classify r eversible dynamical systems, and reduce their (Ideal) study to that of reversible normal forms.