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Titlebook: Applications of Centre Manifold Theory; Jack Carr Book 1982 Springer-Verlag New York Inc. 1982 Calc.Calculation.Differentialgleichung.Fini

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期刊全称Applications of Centre Manifold Theory
影响因子2023Jack Carr
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学科分类Applied Mathematical Sciences
图书封面Titlebook: Applications of Centre Manifold Theory;  Jack Carr Book 1982 Springer-Verlag New York Inc. 1982 Calc.Calculation.Differentialgleichung.Fini
影响因子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
Pindex Book 1982
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https://doi.org/10.1007/978-1-4612-5929-9Calc; Calculation; Differentialgleichung; Finite; Mannigfaltigkeit; Verzweigung; applied mathematics; diffe
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978-0-387-90577-8Springer-Verlag New York Inc. 1982
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Michael J. Murray,Mathew ForstaterIn this chapter we state the main results of centre manifold theory for finite dimensional systems and give some simple examples to illustrate their application.
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Introduction to Centre Manifold Theory,In this chapter we state the main results of centre manifold theory for finite dimensional systems and give some simple examples to illustrate their application.
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Examples,In this section we study the decay to zero of solutions of the equation . where f is a smooth function with . where a is a constant. By using a suitable Liapunov function it is easy to show that the zero solution of (3.1.1) is asymptotically stable. However, because f′(0) = 0, the rate of decay cannot be determined by linearization.
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