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Methods and Concepts

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

Abstract

Center manifolds facilitate the reduction of the dimension of a bifurcation problem to the necessary minimum. The local center manifold of an equilibrium, i.e. the bifurcation point, is a smooth manifold tangential to the center eigenspace of that equilibrium. The center eigenspace is the generalized eigenspace to all purely imaginary (or zero) eigenvalues of the linearization of the vector field at the equilibrium. The local center manifold contains all bounded solution in a small neighborhood, in particular all equilibria, all periodic orbits, and all connecting (heteroclinic) orbits of equilibria.

Keywords

  • Vector Field
  • Normal Form
  • Taylor Expansion
  • Center Manifold
  • Bifurcation Problem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Liebscher, S. (2015). Methods and Concepts. In: Bifurcation without Parameters. Lecture Notes in Mathematics, vol 2117. Springer, Cham. https://doi.org/10.1007/978-3-319-10777-6_2

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