LEADER 03879nam 2200601 450 001 9910480687103321 005 20170816143318.0 010 $a1-4704-0844-9 035 $a(CKB)3360000000464605 035 $a(EBL)3113822 035 $a(SSID)ssj0000889289 035 $a(PQKBManifestationID)11549053 035 $a(PQKBTitleCode)TC0000889289 035 $a(PQKBWorkID)10876976 035 $a(PQKB)10015300 035 $a(MiAaPQ)EBC3113822 035 $a(PPN)195413040 035 $a(EXLCZ)993360000000464605 100 $a20140903h19901990 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aUnfoldings and bifurcations of quasi-periodic tori /$fH.W. Broer [and three others] 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d1990. 210 4$dİ1990 215 $a1 online resource (189 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 83, Number 421 300 $a"January 1990, volume 83, number 421 (third of 6 numbers)." 311 $a0-8218-2483-X 320 $aIncludes bibliographical references. 327 $a""TABLE OF CONTENTS""; ""PART I: UNFOLDINGS OF QUASIa???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"" 327 $a""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. Applicationsa???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)]a???action""; ""f. Oscillators with quasia???periodic forcing""; ""8. Proof of the main result""; ""a. Introduction""; ""b. Proof of Theorem 8.1""; ""c. Proof of Theorem 6.1""; ""Appendix"" 327 $a""Finite differentiability""""PART II: TOWARD A QUASIa???PERIODIC BIFURCATION THEORY""; ""1. Introduction""; ""2. A higher order normal form theory""; ""a. The case m = 1""; ""b. The case m = 2""; ""c. Whitneya???smoothness in the frequencies""; ""d. The local approach""; ""3. The bifurcation models""; ""a. Preliminaries""; ""b. The quasia???periodic perioda???doubling bifurcation""; ""c. The quasia???periodic Hopfa???bifurcation""; ""d. The quasia???periodic saddlea???node bifurcation""; ""4. Applications""; ""a. Oscillators with quasia???periodic forcing""; ""b. Local bifurcations"" 327 $a""5. Proof of the Saddlea???Node Stability Theorem""""a. Formulation""; ""b. Transfer of the perturbation problem""; ""c. Proof""; ""Appendix""; ""References"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 83, Number 421. 606 $aFlows (Differentiable dynamical systems) 606 $aBifurcation theory 606 $aTorus (Geometry) 608 $aElectronic books. 615 0$aFlows (Differentiable dynamical systems) 615 0$aBifurcation theory. 615 0$aTorus (Geometry) 676 $a515/.352 702 $aBroer$b H. W$g(Hendrik Wolter),$f1950- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480687103321 996 $aUnfoldings and bifurcations of quasi-periodic tori$92150736 997 $aUNINA