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Field name	Details
Dewey Class	514.34
Title	Applications of Centre Manifold Theory ([EBook] /) / by Jack Carr.
Author	Carr, Jack
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : : Springer US, , 1982.
Physical Details	XIV, 142 p. : online resource.
Series	Applied mathematical sciences 0066-5452 ; ; 35
ISBN	9781461259299
Summary Note	These 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).:
Contents note	0 -- 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4612-5929-9
Links to Related Works	Subject References: Complex manifolds . Manifolds and Cell Complexes (incl. Diff.Topology) . Manifolds (Mathematics) . Mathematics . Authors: Carr, Jack . Corporate Authors: SpringerLink (Online service) . Series: Applied mathematical sciences . Classification: 514.34 .

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Applications of Centre Manifold Theory

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