Canonical coordinate systems and exponential maps of <i>n</i>-loop

Abstract

This paper is devoted to the study of canonical coordinate systems and the corresponding exponential maps of n-ary differentiable loops and to the discussion of their differentiability properties. Canonical coordinate systems can be determined by the canonical normal form of the power series expansion of the n-th power map $x → x ○ x ○ ... ○ x ○ x$.