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Summary and Outlook

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

Abstract

Along given manifolds of equilibria, bifurcations without parameters display a surprisingly rich and intricate structure of heteroclinic connections. Although manifolds of equilibria appear to be a rather degenerate feature of a vector field, the large variety of applications exhibiting this structure requires a systematic analysis of the emerging bifurcation problems. Techniques including center manifolds, normal forms and blow-up methods are indispensable for the theory.

Keywords

  • Vector Field
  • Bifurcation Point
  • Bifurcation Theory
  • Heteroclinic Orbit
  • Heteroclinic Connection

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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References

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© 2015 Springer International Publishing Switzerland

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Liebscher, S. (2015). Summary and Outlook. In: Bifurcation without Parameters. Lecture Notes in Mathematics, vol 2117. Springer, Cham. https://doi.org/10.1007/978-3-319-10777-6_16

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