Abstract
In this chapter we present a number of results from the theory of normal forms. The idea of normal forms consists in finding a polynomial change of variable which “improves” locally a nonlinear system, in order to more easily recognize its dynamics. As we shall see, normal form transformations apply to general classes of nonlinear systems in ℝn near a fixed point, here the origin, by just assuming a certain smoothness of the vector field. In particular, this theory applies to the reduced systems provided by the center manifold theory given in the previous chapter.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 EDP Sciences
About this chapter
Cite this chapter
Haragus, M., Iooss, G. (2011). Normal Forms. In: Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems. Universitext. Springer, London. https://doi.org/10.1007/978-0-85729-112-7_3
Download citation
DOI: https://doi.org/10.1007/978-0-85729-112-7_3
Publisher Name: Springer, London
Print ISBN: 978-0-85729-111-0
Online ISBN: 978-0-85729-112-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)