LEADER 04657nam 2200601 450 001 9910788759303321 005 20170816143339.0 010 $a1-4704-0159-2 035 $a(CKB)3360000000464758 035 $a(EBL)3113995 035 $a(SSID)ssj0000889254 035 $a(PQKBManifestationID)11932402 035 $a(PQKBTitleCode)TC0000889254 035 $a(PQKBWorkID)10876590 035 $a(PQKB)11410204 035 $a(MiAaPQ)EBC3113995 035 $a(RPAM)1146061 035 $a(PPN)19541456X 035 $a(EXLCZ)993360000000464758 100 $a20140908h19961996 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSymmetry breaking for compact Lie groups /$fMichael Field 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d1996. 210 4$dİ1996 215 $a1 online resource (185 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vNumber 574 300 $a"March 1996, Volume 120, Number 574 (second of 4 numbers)." 311 $a0-8218-0435-9 320 $aIncludes bibliographical references. 327 $a""Contents""; ""1. Introduction""; ""1.1. Notes for the reader""; ""1.2. Acknowledgements""; ""2. Technical Preliminaries and Basic Notations""; ""2.1. I??-sets and isotropy types""; ""2.2. Representations""; ""2.3. Isotropy types for representations""; ""2.4. Polynomial Invariants and Equivariants""; ""2.5. Smooth families of equivariant maps""; ""2.6. Normalized families""; ""3. Branching and invariant group orbits""; ""3.1. Relative equilibria and normal hyperbolicity""; ""3.2. Branches of relative equilibria""; ""3.3. The branching pattern""; ""3.4. Stabilities"" 327 $a""3.5. Branching conditions""""3.6. The signed indexed branching pattern""; ""3.7. Stable families""; ""3.8. Determinacy""; ""3.9. Strong determinacy""; ""4. Genericity theorems""; ""4.1. Semi-algebraic and semi-analytic sets""; ""4.2. Invariant and equi variant generators""; ""4.3. The variety I?£""; ""4.4. Stability theorems I: Weak regularity""; ""4.5. Stability theorems II: Regular families""; ""4.6. Determinacy""; ""4.7. Examples related to finite reflection groups""; ""5. Finitely determined bifurcation problems I""; ""5.1. The phase vector field"" 327 $a""5.2. The spaces A[sub(h)](I??,V), B[sub(h)](I??,V)""""5.3. Strong determinacy""; ""6. Finitely-determined bifurcation problems II""; ""6.1. Statement of the main theorem""; ""6.2. 2-stable relative equilibria""; ""7. Strong determinacy: Technical preliminaries""; ""7.1. Introduction""; ""7.2. Notational conventions""; ""7.3. Local geometry""; ""7.4. Weakly regular families""; ""7.5. Analytic families and solution branches""; ""7.6. Compatible parametrizations and initial exponents""; ""7.7. Remarks on the set I??(f)""; ""7.8. The parametrization theorem""; ""7.9. The space R[sup(2)]"" 327 $a""7.10. Initial exponents and the space R[sup(3)]""""8. Strong determinacy: I?? finite""; ""8.1. Analytic parametrizations""; ""8.2. Estimates on eigenvalues""; ""8.3. Fractional power series""; ""8.4. Eigenvalue estimates: Analytic case""; ""8.5. Eigenvalue estimates: Smooth case""; ""8.6. Proof of Theorem 8.2.6""; ""8.7. Strong determinacy: I?? finite""; ""8.8. Formation of new branches under perturbation""; ""9. Strong determinacy: I?? compact, non-finite""; ""9.1. Polar blowing-up: Local theory""; ""9.2. Polar blowing-up: Global theory""; ""9.3. Polar blowing-up a I??-manifold"" 327 $a""9.4. Blowing- up""""9.4.1. Blowing-up along a linear subspace""; ""9.4.2. Blowing-up analytic varieties""; ""9.4.3. Blowing-up algebraic varieties""; ""9.5. Conical sets""; ""9.6. Algebraic and analytic structure of the orbit strata""; ""9.7. Blowing-up representations""; ""9.7.1. Analytic theory""; ""9.7.2. Algebraic theory""; ""9.8. A tangent and normal decomposition""; ""9.9. Blowing-up arcs""; ""9.10. Analytic parametrizations of solution branches""; ""9.11. Lifting analytic parametrizations""; ""9.12. Controlling the lifts of analytic parametrizations"" 327 $a""9.13. Symmetric structure of parametrizations"" 410 0$aMemoirs of the American Mathematical Society ;$vNumber 574. 606 $aBifurcation theory 606 $aLie groups 615 0$aBifurcation theory. 615 0$aLie groups. 676 $a515/.353 700 $aField$b Mike$056769 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788759303321 996 $aSymmetry breaking for compact Lie groups$93835306 997 $aUNINA