1307.3368 (Andrey Nikolaev)

Kato perturbation expansion in classical mechanics and explicit
expression for Deprit generator    [PDF]

Andrey Nikolaev

This work explores structure of Poincare-Lindstedt perturbation series in Deprit operator formalism and establishes its connection to Kato resolvent expansion. It discusses invariant definitions of averaging and integrating perturbation operators and their canonical identities. This reveals regular pattern in Deprit generator. Abel averaging relates perturbation operators to Laurent coefficients of resolvent of Liouville operator and Kato series. This purely canonical approach systematizes the perturbation expansion and leads to explicit expression for Deprit generator of Poincare-Lindstedt transformation. Non-perturbative examples used as illustration.

View original: http://arxiv.org/abs/1307.3368