Advertisement

Bifurcation near Equilibrium

  • Shui-Nee Chow
  • Jack K. Hale
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 251)

Abstract

In this chapter, we discuss various types of dynamic behavior when a bifurcation arises from the existence of a simple eigenvalue. More specificially, we consider an equation
$$ Cx + N(x,\mu ) = 0 $$
(1.1)
in a Banach space X for μ in a Banach space E, N(0, 0) = 0, N(0, 0)/x = 0 under the assumption that the linear operator C has zero as a simple eigen-value. The method of Liapunov—Schmidt gives a scalar bifurcation function G(a, μ) defined for (a, μ) in neighborhood of (0, 0) ∈ ℝ × E. Suppose Cx + N(x, μ)is the vector field for an evolutionary equation
$$ \tfrac{{dx}}{{dt}} = Cx + N(x,\mu ) $$
(1.2)
.

Keywords

Banach Space Periodic Solution Periodic Orbit Equilibrium Point Stability Property 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • Shui-Nee Chow
    • 1
  • Jack K. Hale
    • 2
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA
  2. 2.Division of Applied MathematicsBrown UniversityProvidenceUSA

Personalised recommendations