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Bifurcation theory : an introduction with applications to PDEs

Autor: Hansjörg Kielhöfer
Editorial: New York : Springer, ©2003.
Serie: Applied mathematical sciences (Springer-Verlag New York Inc.), v. 156.
Edición/Formato:   book_printbook : Inglés (eng)Ver todas las ediciones y todos los formatos
Base de datos:WorldCat
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Tipo de material: Recurso en Internet
Tipo de documento: Libro/Texto, Recurso en Internet
Todos autores / colaboradores: Hansjörg Kielhöfer
ISBN: 0387404015 9780387404011
Número OCLC: 52430721
Descripción: pages cm.
Contenido: I. Local theory --
1. The implicit function theorem --
2. The method of Lyapunov-Schmidt --
3. The Lyapunov-Schmidt reduction for potential operators --
4. An implicit function theorem for one-dimensional Kernels: Turning points --
5. Bifurcation with a one-dimensional Kernel --
6. Bifurcation formulas (stationary case) --
7. The principle of exchange of stability (stationary case) --
8. Hopf bifurcation --
9. Bifurcation formulas for Hopf bifurcation --
10. A Lyapunov center theorem --
11. Constrained Hopf bifurcation for Hamiltonian, reversible, and conservative systems --
12. The principle of exchange of stability for Hopf bifurcation --
13. Continuation of periodic solutions --
14. Period-doubling bifurcation and exchange of stability --
15. The Newton polygon --
16. Degenerate bifurcation at a simple Eigenvalue and stability of bifurcating solutions --
17. Degenerate Hopf bifurcation and Floquet exponents of bifurcating periodic orbits --
18. The principle of reduced stability for stationary and periodic solutions --
19. Bifurcation with high-dimensional Kernels, multiparameter bifurcation, and application of the principle of reduced stability --
20. Bifurcation from infinity --
21. Bifurcation with high-dimensional Kernels for potential operators: Variational methods --
22. Notes and remarks to chapter I --
II. Global theory --
1. The Brouwer degree --
2. The Leray-Schauder degree --
3. Application of the degree in bifurcation theory --
4. Odd crossing numbers --
5. A degree for a class of proper Fredholm operators and global bifurcation theorems --
6. A global implicit function theorem --
7. Change of Morse index and local bifurcation for potential operators --
8. Notes and remarks to chapter II --
III. Applications --
1. The Fredholm property of elliptic operators --
2. Local bifurcation for elliptic problems --
3. Free nonlinear vibrations --
4. Hopf bifurcation for parabolic problems --
5. Global bifurcation and continuation for elliptic problems --
6. Preservation of nodal structure on global branches --
7. Smoothness and uniqueness of global positive solution branches --
8. Notes and remarks to chapter III.
Título de la serie: Applied mathematical sciences (Springer-Verlag New York Inc.), v. 156.
Responsabilidad: Hansjörg Kielhöfer.
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