Author | Marsden, J. E. author |
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Title | The Hopf Bifurcation and Its Applications [electronic resource] / by J. E. Marsden, M. McCracken |
Imprint | New York, NY : Springer New York, 1976 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-6374-6 |
Descript | 408 p. online resource |
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 Poincarรฉ 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 Hopfโs 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 Hopfโs 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 Kirchgรคssner and Kielhรถffer -- Section 10 Bifurcation Phenomena in Population Models -- Section 11 A Mathematical Model of Two Cells -- Section 12 A Strange, Strange Attractor -- References