Spectral sequences and parametric normal forms

Spectral sequences and parametric normal forms

Article history: Received 19 November 2010 Revised 10 September 2011 Available online 19 October 2011 MSC: 34C20 34A34 16W5 68U99

Formal Decomposition Method and Parametric Normal Forms

We introduce a formal decomposition method for efficiently computing the parametric normal form of nonlinear dynamical systems with multiple parameters. Recently introduced notions of formal basis style and costyle are applied through formal decomposition method to obtain the simplest parametric normal form for degenerate nonlinear parametric center. The necessary formulas are derived and imple...

Normal form theory and spectral sequences

The goal of this paper is to show that spectral sequences give us a natural language in which to describe the process of computing the unique normal form. For a solid modern introduction to normal form theory and its historical development, see [Mur03b]. Although this is in no way intended as a review of (unique) normal form theory, let me give the reader some references to the literature which...

A Spectral Sequence Approach to Normal Forms

Normal forms for three-dimensional parametric instabilities in ideal hydrodynamics

We derive and analyze several low dimensional Hamiltonian normal forms describing system symmetry breaking in ideal hydrodynamics. The equations depend on two parameters (e,2), where e is the strength of a system symmetry breaking perturbation and 2 is a detuning parameter. In many cases the resulting equations are completely integrable and have an interesting Hamiltonian structure. Our work is...