| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910788744103321 |
|
|
Autore |
Celletti A (Alessandra) |
|
|
Titolo |
KAM stability and celestial mechanics / / Alessandra Celletti, Luigi Chierchia |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Providence, Rhode Island : , : American Mathematical Society, , 2007 |
|
©2007 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Descrizione fisica |
|
1 online resource (150 p.) |
|
|
|
|
|
|
Collana |
|
Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 187, Number 878 |
|
|
|
|
|
|
|
|
Classificazione |
|
|
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Three-body problem |
Celestial mechanics |
Perturbation (Mathematics) |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
"Volume 187, Number 878 (third of four numbers)." |
|
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references. |
|
|
|
|
|
|
Nota di contenuto |
|
""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"" |
""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"" |
""4.1. Iso-energetic Lindstedt series for the Sun-Jupiter-Asteroid problem and choice of the initial approximate tori (u[sup((0)±)], v[sup |
|
|
|
|
|
|
|
|
|
|
((0)±)], w[sup((0)±)])""""4.2. Evaluation of the input parameters of the KAM norm map associated to the approximate tori (u[sup((0)±)], v[sup((0)±)], w[sup((0)±)])""; ""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"" |
""B.2. Estimates on s[sub(p)],k(Î?)""""Appendix C. Interval Arithmetic""; ""Appendix D. A Guide to the Computer Programs""; ""Bibliography"" |
|
|
|
|
|
| |