The spectral sequences and parametric normal forms

TL;DR

This paper develops a theoretical framework for parametric normal forms using spectral sequences, introducing new styles for uniqueness, and applies these methods to systems with multiple parameters.

Contribution

It generalizes spectral sequences for parametric normal forms and introduces new styles to ensure their uniqueness, with applications to generalized Hopf singularities.

Findings

Established a foundation for parametric normal forms.

Introduced new styles and costyles for uniqueness.

Applied methods to systems with multiple parameters.

Abstract

We generalize recent developments on normal forms and the spectral sequences method to make a foundation for parametric normal forms. We further introduce a new style and costyle to obtain unique parametric normal forms. The results are applied to systems of generalized Hopf singularity with multiple parameters. A different (new) version of this paper has been submitted for a possible publication in a refereed journal.