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Codimension-One Manifolds of Equilibria

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2117)

Abstract

Here we discuss a special situation in which we can deal with singularities of arbitrary codimension. In Chaps. 4, 8, and after normal form transformation also in Chaps. 5, 9, we removed the manifold of equilibria by multiplying with a singular factor 1∕x or 1∕r. This idea required that there is only one transverse direction to the manifold of equilibria. For such manifolds of codimension one, in phase space, we can generalize the idea.

Keywords

  • Differential Equation
  • Dynamical System
  • Phase Space
  • Partial Differential Equation
  • Ordinary Differential Equation

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References

  1. Bruce, J., Giblin, P.: Curves and Singularities, 2nd edn. Cambridge University Press, Cambridge (1992)

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© 2015 Springer International Publishing Switzerland

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Liebscher, S. (2015). Codimension-One Manifolds of Equilibria. In: Bifurcation without Parameters. Lecture Notes in Mathematics, vol 2117. Springer, Cham. https://doi.org/10.1007/978-3-319-10777-6_15

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