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

Kato perturbation expansion in classical mechanics and an explicit expression for a Deprit generator