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Unfoldings and bifurcations of quasi-periodic tori /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
1990.
|
| Colección: | Memoirs of the American Mathematical Society ;
Volume 83, no. 421. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- ""TABLE OF CONTENTS""; ""PART I: UNFOLDINGS OF QUASI�PERIODIC TORI""; ""1. Introduction""; ""2. Preliminaries""; ""a. Invariant manifolds, normal linearization, integrability""; ""b. Unfoldings of matrices""; ""3. The integrable case""; ""a. The general (dissipative) context""; ""b. The volume preserving context""; ""c. The symplectic context""; ""4. The nearly integrable case in the general (dissipative) context""; ""5. The nearly integrable cases in the volume preserving and the symplectic (m = n) contexts""; ""a. Addition of local parameters""; ""b. The volume preserving case m = 1""
- ""C. The symplectic case m = n""""6. The nearly integrable case in the general symplectic context""; ""a. General remarks""; ""b. Normal linearization""; ""c. The results""; ""7. Applications�Related results""; ""a. A more general stability result""; ""b. Comparison with Moser's modifying terms""; ""c. Fewer parameters""; ""d. Applications to local bifurcation theory""; ""e. A locally free [omitted][sup(n)]�action""; ""f. Oscillators with quasi�periodic forcing""; ""8. Proof of the main result""; ""a. Introduction""; ""b. Proof of Theorem 8.1""; ""c. Proof of Theorem 6.1""; ""Appendix""
- ""Finite differentiability""""PART II: TOWARD A QUASI�PERIODIC BIFURCATION THEORY""; ""1. Introduction""; ""2. A higher order normal form theory""; ""a. The case m = 1""; ""b. The case m = 2""; ""c. Whitney�smoothness in the frequencies""; ""d. The local approach""; ""3. The bifurcation models""; ""a. Preliminaries""; ""b. The quasi�periodic period�doubling bifurcation""; ""c. The quasi�periodic Hopf�bifurcation""; ""d. The quasi�periodic saddle�node bifurcation""; ""4. Applications""; ""a. Oscillators with quasi�periodic forcing""; ""b. Local bifurcations""
- ""5. Proof of the Saddle�Node Stability Theorem""""a. Formulation""; ""b. Transfer of the perturbation problem""; ""c. Proof""; ""Appendix""; ""References""