  This work explores the structure of Poincare-Lindstedt perturbation series in
Deprit operator formalism and establishes its connection to Kato resolvent
expansion. A discussion of invariant definitions for averaging and integrating
perturbation operators and their canonical identities reveals a regular pattern
in a Deprit generator. The pattern was explained using Kato series and the
relation of perturbation operators to Laurent coefficients for the resolvent of
Liouville operator.
  This purely canonical approach systematizes the series and leads to the
explicit expression for the Deprit generator in any perturbation order: \[G = -
\hat{\mathsf S}_H H_i.\] Here, $\hat{\mathsf S}_H$ is the partial
pseudo-inverse of the perturbed Liouville operator. Corresponding Kato series
provides a reasonably effective computational algorithm.
  The canonical connection of perturbed and unperturbed averaging operators
allows for a description of ambiguities in the generator and transformed
Hamiltonian, while Gustavson integrals turn out to be insensitive to
normalization style. Non-perturbative examples are used for illustration.
