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OverviewThese notes are based on a series of lectures given in the Lefschetz Center for Dynamical Systems in the Division of Applied Mathematics at Brown University during the academic year 1978-79. The purpose of the lectures was to give an introduction to the applications of centre manifold theory to differential equations. Most of the material is presented in an informal fashion, by means of worked examples in the hope that this clarifies the use of centre manifold theory. The main application of centre manifold theory given in these notes is to dynamic bifurcation theory. Dynamic bifurcation theory is concerned with topological changes in the nature of the solutions of differential equations as para meters are varied. Such an example is the creation of periodic orbits from an equilibrium point as a parameter crosses a critical value. In certain circumstances, the application of centre manifold theory reduces the dimension of the system under investigation. In this respect the centre manifold theory plays the same role for dynamic problems as the Liapunov-Schmitt procedure plays for the analysis of static solutions. Our use of centre manifold theory in bifurcation problems follows that of Ruelle and Takens [57) and of Marsden and McCracken [51). Full Product DetailsAuthor: J. CarrPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 1982 ed. Volume: 35 Dimensions: Width: 15.50cm , Height: 0.80cm , Length: 23.50cm Weight: 0.520kg ISBN: 9780387905778ISBN 10: 0387905774 Pages: 142 Publication Date: 29 June 1981 Audience: College/higher education , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents0.- 4.5. The Case ?1 < 0.- 4.6. More Scaling.- 4.7. Completion of the Phase Portraits.- 4.8. Remarks and Exercises.- 4.9. Quadratic Nonlinearities.- 5. Application to a Panel Flutter Problem.- 5.1. Introduction.- 5.2. Reduction to a Second Order Equation.- 5.3. Calculation of Linear Terms.- 5.4. Calculation of the Nonlinear Terms.- 6. Infinite Dimensional Problems.- 6.1. Introduction.- 6.2. Semigroup Theory.- 6.3. Centre Manifolds.- 6.4. Examples.- References.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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