Hopf Bifurcation with Symmetry

  • Martin Golubitsky
  • Ian Stewart
Part of the Progress in Mathematics book series (PM, volume 200)


In the previous chapter we studied the symmetry properties of time-periodic states of equivariant dynamical systems. We did not enquire how such states might arise. In this chapter we develop the theory of one of the most widespread routes to time-periodicity: Hopf bifurcation. The physical characteristics of Hopf bifurcation are the loss of stability of a steady state, as a parameter is varied, leading to a bifurcation to small-amplitude periodic states with `finite period’. That is, the limiting period as the amplitude tends to zero (immediately after bifurcation) is finite and nonzero


Periodic Solution Hopf Bifurcation Loop Space Spiral Wave Inverse Limit 
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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • Martin Golubitsky
    • 1
  • Ian Stewart
    • 2
  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

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