# Normalization in Banach scale Lie algebras via mould calculus and applications

@article{Paul2016NormalizationIB, title={Normalization in Banach scale Lie algebras via mould calculus and applications}, author={Thierry Paul and David Sauzin}, journal={arXiv: Analysis of PDEs}, year={2016} }

We study a perturbative scheme for normalization problems involving resonances of the unperturbed situation, and therefore the necessity of a non-trivial normal form, in the general framework of Banach scale Lie algebras (this notion is defined in the article). This situation covers the case of classical and quantum normal forms in a unified way which allows a direct comparison. In particular we prove a precise estimate for the difference between quantum and classical normal forms, proven to be… Expand

#### 4 Citations

Normalization in Lie algebras via mould calculus and applications

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We establish Écalle’s mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical… Expand

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