Unfoldings and bifurcations of quasi-periodic tori

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

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Bibliographic Details
Main Author: Broer, H. W. (Hendrik Wolter), 1950- (Author)
Format: eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, 1990.
Series:Memoirs of the American Mathematical Society ; Volume 83, no. 421.
Subjects:
Flows (Differentiable dynamical systems)
Bifurcation theory.
Torus (Geometry)
Bifurcation theory
Online Access:Click for online access
Table of Contents:
  • ""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""

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