Author | Iooss, Gรฉrard. author |
---|---|

Title | Elementary Stability and Bifurcation Theory [electronic resource] / by Gรฉrard Iooss, Daniel D. Joseph |

Imprint | New York, NY : Springer New York : Imprint: Springer, 1980 |

Connect to | http://dx.doi.org/10.1007/978-1-4684-9336-8 |

Descript | XV, 286 p. online resource |

SUMMARY

In its most general form bifurcation theory is a theory of equilibrium solutions of nonlinear equations. By equilibrium solutions we mean, for example, steady solutions, time-periodic solutions, and quasi-periodic solutions. The purpose of this book is to teach the theory of bifurcation of equilibrium solutions of evolution problems governed by nonlinear differential equations. We have written this book for the broaqest audience of potentially interested learners: engineers, biologists, chemists, physicists, mathematicians, economยญ ists, and others whose work involves understanding equilibrium solutions of nonlinear differential equations. To accomplish our aims, we have thought it necessary to make the analysis 1. general enough to apply to the huge variety of applications which arise in science and technology, and 2. simple enough so that it can be understood by persons whose matheยญ matical training does not extend beyond the classical methods of analysis which were popular in the 19th Century. Of course, it is not possible to achieve generality and simplicity in a perfect union but, in fact, the general theory is simpler than the detailed theory required for particular applications. The general theory abstracts from the detailed problems only the essential features and provides the student with the skeleton on which detailed structures of the applications must rest. It is generally believed that the mathematical theory of bifurcation requires some functional analysis and some of the methods of topology and dynamics

CONTENT

I Equilibrium Solutions of Evolution Problems -- II Bifurcation and Stability of Steady Solutions of Evolution Equations in One Dimension -- III Imperfection Theory and Isolated Solutions Which Perturb Bifurcation -- IV Stability of Steady Solutions of Evolution Equations in Two Dimensions and n Dimensions -- V Bifurcation of Steady Solutions in Two Dimensions and the Stability of the Bifurcating Solutions -- VI Methods of Projection for General Problems of Bifurcation into Steady Solutions -- VII Bifurcation of Periodic Solutions from Steady Ones (Hopf Bifurcation) in Two Dimensions -- VIII Bifurcation of Periodic Solutions in the General Case -- IX Subharmonic Bifurcation of Forced T-Periodic Solutions -- X Bifurcation of Forced T-Periodic Solutions into Asymptotically Quasi-Periodic Solutions -- XI Secondary Subharmonic and Asymptotically Quasi-Periodic Bifurcation of Periodic Solutions of (Hopfโ{128}{153}s Type) in the Autonomous Case

Physics
Mathematical analysis
Analysis (Mathematics)
Physics
Theoretical Mathematical and Computational Physics
Analysis