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Normal Forms and Invariant Manifolds

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Methods of Bifurcation Theory

Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 251))

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Abstract

In the previous chapter, we began the discussion of the bifurcations that occur in nonautonomous perturbations of autonomous equations. To understand more about these bifurcations, we need several general results and methods from the theory of differential equations—in particular, the theory of transformation to normal form and the method of integral manifolds. This material is also an important ingredient in the discussion in the next chapter on the behavior near an equilibrium point in dimension greater than two for which the linear variational equation has several eigenvalues on the imaginary axis.

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© 1982 Springer-Verlag New York Inc.

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Chow, SN., Hale, J.K. (1982). Normal Forms and Invariant Manifolds. In: Methods of Bifurcation Theory. Grundlehren der mathematischen Wissenschaften, vol 251. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8159-4_12

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  • DOI: https://doi.org/10.1007/978-1-4613-8159-4_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8161-7

  • Online ISBN: 978-1-4613-8159-4

  • eBook Packages: Springer Book Archive

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