Abstract
We shall give here, following Lanford [1], an elementary and straightforward derivation of the canonical form for the mapping Φµ: ℝ2 → ℝ2. Recall that we have already arranged things so that
We want to organize the second, third, and fourth degree terms by making further coordinate changes. It will be convenient to identify R2 with the complex plane by writing
Then
From now on we shall leave y out of our notation as much as possible.
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
Rights and permissions
Copyright information
© 1976 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Marsden, J.E., McCracken, M. (1976). The Canonical Form. In: The Hopf Bifurcation and Its Applications. Applied Mathematical Sciences, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6374-6_16
Download citation
DOI: https://doi.org/10.1007/978-1-4612-6374-6_16
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90200-5
Online ISBN: 978-1-4612-6374-6
eBook Packages: Springer Book Archive