LEADER 04531nam 2200577 450 001 996320722703316 005 20170929022337.0 010 $a0-8218-1633-0 010 $a0-8218-3208-5 035 $a(CKB)1000000000523287 035 $a(EBL)3112757 035 $a(MiAaPQ)EBC3112757 035 $a(RPAM)3665473 035 $a(PPN)193128462 035 $a(EXLCZ)991000000000523287 100 $a20770429h19771977 uy| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aGeometric asymptotics /$fby Victor Guillemin and Shlomo Sternberg 205 $aRevised ed. 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[1977] 210 4$dİ1977 215 $a1 online resource (500 p.) 225 1 $aMathematical surveys and monographs ;$vnumber 14 300 $aDescription based upon print version of record. 320 $aIncludes bibliographical references and index. 327 $a""TABLE OF CONTENTS""; ""PREFACE""; ""NOTATION""; ""CHAPTER I. INTRODUCTION. THE METHOD OF STATIONARY PHASE""; ""APPENDIX I. MORSE'S LEMMA AND SOME GENERALIZATIONS""; ""CHAPTER II. DIFFERENTIAL OPERATORS AND ASYMPTOTIC SOLUTIONS""; ""A?1. Differential operators""; ""A?2. Asymptotic sections""; ""A?3. The LA?neburg-Lax-Ludwig technique""; ""A?4. The methods of characteristics""; ""A?5. Bi-characteristics""; ""A?6. The transport equation""; ""A?7. The Maslov cycle and the Bohr-Sommerfeld quantization conditions""; ""CHAPTER III. GEOMETRICAL OPTICS"" 327 $a""A?1. The laws of refraction and reflection""""A?2. Focusing and magnification""; ""A?3. Hamilton's method""; ""A?4. First order optics""; ""A?5. The Seidel aberrations""; ""A?6. The asymptotic solution of Maxwell's equations""; ""CHAPTER IV. SYMPLECTIC GEOMETRY""; ""A?1. The Darboux-Weinstein theorem""; ""A?2. Symplectic vector spaces""; ""A?3. The cross index and the Maslov class""; ""A?4. Functorial properties of Lagrangian submanifolds""; ""A?5. Local parametrizations of Lagrangian submanifolds""; ""A?6. Periodic Hamiltonian systems""; ""A?7. Homogeneous symplectic spaces"" 327 $a""A?8. Multisymplectic structures and the calculus of variations""""CHAPTER V. GEOMETRIC QUANTIZATION""; ""A?1. Curvature forms and vector bundles""; ""A?2. The group of automorphisms of an Hermitian line bundle""; ""A?3. Polarizations""; ""A?4. Metalinear manifolds and half forms""; ""A?5. Metaplectic manifolds""; ""A?6. The pairing of half form sections""; ""A?7. The metaplectic representation""; ""A?8. Some examples""; ""CHAPTER VI. GEOMETRIC ASPECTS OF DISTRIBUTIONS""; ""A?1. Elementary functorial properties of distributions""; ""A?2. Traces and characters""; ""A?3. The wave front set"" 327 $a""A?4. Lagrangian distributions """"A?5. The symbol calculus""; ""Appendix to Section 5""; ""A?6. Fourier integral operators""; ""A?7. The transport equation""; ""A?8. Some applications to spectral theory""; ""APPENDIX TO CHAPTER VI. THE PLANCHEREL FORMULA FOR THE COMPLEX SEMI-SIMPLE LIE GROUPS""; ""CHAPTER VII. COMPOUND ASYMPTOTICS""; ""A?0. Introduction""; ""A?1. The asymptotic Fourier transform""; ""A?2. The frequency set""; ""A?3. Functorial properties of compound asymptotics""; ""A?4. The symbol calculus""; ""A?5. Pointwise behavior of compound asymptotics and Bernstein's theorem"" 327 $a""Appendix to Section 5 of Chapter VII""""A?6. Behavior near caustics""; ""A?7. Iterated S[sub(1)] and S[sub(2,0)] singularities, computations""; ""A?8. Proofs of the normal forms""; ""A?9. Behavior near caustics (continued)""; ""APPENDIX II. VARIOUS FUNCTORIAL CONSTRUCTIONS""; ""A?1. The category of smooth vector bundles""; ""A?2. The fiber product""; ""INDEX""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""O""; ""P""; ""R""; ""S""; ""T""; ""U""; ""W"" 410 0$aMathematical surveys and monographs ;$vnumber 14. 606 $aGeometry, Differential 606 $aAsymptotic expansions 606 $aGeometrical optics 615 0$aGeometry, Differential. 615 0$aAsymptotic expansions. 615 0$aGeometrical optics. 676 $a516.3/6 700 $aGuillemin$b Victor$f1937-$040563 702 $aSternberg$b Shlomo 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996320722703316 996 $aGeometric asymptotics$9381732 997 $aUNISA