03879nam 2200601 450 991048068710332120170816143318.01-4704-0844-9(CKB)3360000000464605(EBL)3113822(SSID)ssj0000889289(PQKBManifestationID)11549053(PQKBTitleCode)TC0000889289(PQKBWorkID)10876976(PQKB)10015300(MiAaPQ)EBC3113822(PPN)195413040(EXLCZ)99336000000046460520140903h19901990 uy 0engur|n|---|||||txtccrUnfoldings and bifurcations of quasi-periodic tori /H.W. Broer [and three others]Providence, Rhode Island :American Mathematical Society,1990.©19901 online resource (189 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 83, Number 421"January 1990, volume 83, number 421 (third of 6 numbers)."0-8218-2483-X Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;Volume 83, Number 421.Flows (Differentiable dynamical systems)Bifurcation theoryTorus (Geometry)Electronic books.Flows (Differentiable dynamical systems)Bifurcation theory.Torus (Geometry)515/.352Broer H. W(Hendrik Wolter),1950-MiAaPQMiAaPQMiAaPQBOOK9910480687103321Unfoldings and bifurcations of quasi-periodic tori2150736UNINA