Abstract: In this paper we consider quantum motion integrals
depended on the algebraic reconstruction of BPHZ method for
perturbative renormalization in two different procedures. Then based
on Bogoliubov character and Baker-Campbell-Hausdorff (BCH) formula,
we show that how motion integral condition on components
of Birkhoff factorization of a Feynman rules character on Connes-
Kreimer Hopf algebra of rooted trees can determine a family of fixed
point equations.