LEADER 03697nam 2200613 450 001 9910480507803321 005 20170822140221.0 010 $a1-4704-0482-6 035 $a(CKB)3360000000465062 035 $a(EBL)3114181 035 $a(SSID)ssj0000889021 035 $a(PQKBManifestationID)11480057 035 $a(PQKBTitleCode)TC0000889021 035 $a(PQKBWorkID)10867004 035 $a(PQKB)11666288 035 $a(MiAaPQ)EBC3114181 035 $a(PPN)195417674 035 $a(EXLCZ)993360000000465062 100 $a20150417h20072007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aKAM stability and celestial mechanics /$fAlessandra Celletti, Luigi Chierchia 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2007. 210 4$d©2007 215 $a1 online resource (150 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 187, Number 878 300 $a"Volume 187, Number 878 (third of four numbers)." 311 $a0-8218-4169-6 320 $aIncludes bibliographical references. 327 $a""Contents""; ""Chapter 1. Introduction""; ""1.1. Quasi-periodic solutions for the n-body problem""; ""1.2. A stability theorem for the Sun-Jupiter-Victoria system viewed as a restricted, circular, planar three-body problem""; ""1.3. About the proof of the Sun-Jupiter-Victoria stability theorem""; ""1.4. A short history of KAM stability estimates""; ""1.5. A section-by-section summary""; ""Chapter 2. Iso-energetic KAM Theory""; ""2.1. Notations""; ""2.2. KAM tori""; ""2.3. Newton scheme for finding iso-energetic KAM tori""; ""2.4. The KAM Map""; ""2.5. Technical Tools"" 327 $a""2.6. The KAM Norm Map""""2.7. Iso-energetic KAM Theorem""; ""2.8. Iso-energetic Lindstedt series""; ""Chapter 3. The Restricted, Circular, Planar Three-body Problem""; ""3.1. The restricted three-body problem""; ""3.2. Delaunay action-angle variables for the two-body problem""; ""3.3. The restricted, circular, planar three-body problem viewed as nearly-integrable Hamiltonian system""; ""3.4. The Sun-Jupiter-Asteroid problem""; ""Chapter 4. KAM Stability of the Sun-Jupiter-Victoria Problem"" 327 $a""4.1. Iso-energetic Lindstedt series for the Sun-Jupiter-Asteroid problem and choice of the initial approximate tori (u[sup((0)A?±)], v[sup((0)A?±)], w[sup((0)A?±)])""""4.2. Evaluation of the input parameters of the KAM norm map associated to the approximate tori (u[sup((0)A?±)], v[sup((0)A?±)], w[sup((0)A?±)])""; ""4.3. Iterations of the KAM map""; ""4.4. Application of the iso-energetic KAM theorem and perpetual stability of the Sun-Jupiter-Victoria problem""; ""Appendix A. The Ellipse""; ""Appendix B. Diophantine Estimates""; ""B.1. Diophantine estimates for special quadratic numbers"" 327 $a""B.2. Estimates on s[sub(p)],k(I??)""""Appendix C. Interval Arithmetic""; ""Appendix D. A Guide to the Computer Programs""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 187, Number 878. 606 $aThree-body problem 606 $aCelestial mechanics 606 $aPerturbation (Mathematics) 608 $aElectronic books. 615 0$aThree-body problem. 615 0$aCelestial mechanics. 615 0$aPerturbation (Mathematics) 676 $a521 700 $aCelletti$b A$g(Alessandra),$0305617 702 $aChierchia$b Luigi$f1957- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480507803321 996 $aKAM stability and celestial mechanics$92008359 997 $aUNINA