The Hopf Bifurcation and Its Applications by J. E. Marsden (PDF)

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Section 1 Introduction to Stability and Bifurcation in Dynamical Systems and Fluid Dynamics.- Section 2 The Center Manifold Theorem.- Section 2A Some Spectral Theory.- Section 2B The Poincaré Map.- Section 3 The Hopf Bifurcation Theorem in R2 and in Rn.- Section 3A Other Bifurcation Theorems.- Section 3B More General Conditions for Stability.- Section 3C Hopf’s Bifurcation Theorem and the Center Theorem of Liapunov.- Section 4 Computation of the Stability Condition.- Section 4A How to use the Stability Formula; An Algorithm.- Section 4B Examples.- Section 4C Hopf Bifurcation and the Method of Averaging.- Section 5 A Translation of Hopf’s Original Paper.- Section 5A Editorial Comments.- Section 6 The Hopf Bifurcation Theorem Diffeomorphisms.- Section 6A The Canonical Form.- Section 7 Bifurcations with Symmetry.- Section 8 Bifurcation Theorems for Partial Differential Equations.- Section 8A Notes on Nonlinear Semigroups.- Section 9 Bifurcation in Fluid Dynamics and the Problem of Turbulence.- Section 9A On a Paper of G. Iooss.- Section 9B On a Paper of Kirchgässner and Kielhöffer.- Section 10 Bifurcation Phenomena in Population Models.- Section 11 A Mathematical Model of Two Cells.- Section 12 A Strange, Strange Attractor.- References.

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