Unfoldings and bifurcations of quasi-periodic tori / / H.W. Broer [and three others]

• Record Nr.: UNINA9910480687103321
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 1990; ©1990
• ISBN: 1-4704-0844-9
• Descrizione fisica: 1 online resource (189 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 83, Number 421
• Disciplina: 515/.352
• Soggetti: Flows (Differentiable dynamical systems); Bifurcation theory; Torus (Geometry); Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "January 1990, volume 83, number 421 (third of 6 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""TABLE OF CONTENTS""; ""PART I: UNFOLDINGS OF QUASIâ€?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. Applicationsâ€?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)]â€?action""; ""f. Oscillators with quasiâ€?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 QUASIâ€?PERIODIC BIFURCATION THEORY""; ""1. Introduction""; ""2. A higher order normal form theory""; ""a. The case m = 1""; ""b. The case m = 2""; ""c. Whitneyâ€?smoothness in the frequencies""; ""d. The local approach""; ""3. The bifurcation models""; ""a. Preliminaries""; ""b. The quasiâ€?periodic periodâ€?doubling bifurcation""; ""c. The quasiâ€?periodic Hopfâ€?bifurcation""; ""d. The quasiâ€?periodic saddleâ€?node bifurcation""; ""4. Applications""; ""a. Oscillators with quasiâ€?periodic forcing""; ""b. Local bifurcations""; ""5. Proof of the Saddleâ€?Node Stability Theorem""""a. Formulation""; ""b. Transfer of the perturbation problem""; ""c. Proof""; ""Appendix""; ""References""