KAM stability and celestial mechanics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2007
|
| Series: | Memoirs of the American Mathematical Society
878 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "May 2007, volume 187, number 878 (third of 4 numbers)." Includes bibliographical references |
| Physical Description: | VII, 134 S. graph. Darst. |
| ISBN: | 9780821841693 |
Staff View
MARC
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| 245 | 1 | 0 | |a KAM stability and celestial mechanics |c Alessandra Celletti ; Luigi Chierchia |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2007 | |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 878 | |
| 500 | |a "May 2007, volume 187, number 878 (third of 4 numbers)." | ||
| 500 | |a Includes bibliographical references | ||
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| 650 | 4 | |a Three-body problem | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Chapter 1. Introduction 1
1.1. Quasi periodic solutions for the n body problem 1
1.2. A stability theorem for the Sun Jupiter Victoria system viewed as a
restricted, circular, planar three body problem 3
1.3. About the proof of the Sun Jupiter Victoria stability theorem 6
1.4. A short history of KAM stability estimates 8
1.5. A section by section summary 10
Chapter 2. Iso energetic KAM Theory 13
2.1. Notations 13
2.2. KAM tori 15
2.3. Newton scheme for finding iso energetic KAM tori 16
2.4. The KAM Map 27
2.5. Technical Tools 28
2.6. The KAM Norm Map 36
2.7. Iso energetic KAM Theorem 48
2.8. Iso energetic Lindstedt series 70
Chapter 3. The Restricted, Circular, Planar Three body Problem 75
3.1. The restricted three body problem 75
3.2. Delaunay action angle variables for the two body problem 75
3.3. The restricted, circular, planar three body problem viewed as
nearly integrable Hamiltonian system 84
3.4. The Sun Jupiter Asteroid problem 89
Chapter 4. KAM Stability of the Sun Jupiter Victoria Problem 95
4.1. Iso energetic Lindstedt series for the Sun Jupiter Asteroid problem
and choice of the initial approximate tori (u(0)±, a/0)±, w(0)±) 96
4.2. Evaluation of the input parameters of the KAM norm map associated
to the approximate tori (u*0^, «(0)±,w(0)±) 100
4.3. Iterations of the KAM map 108
4.4. Application of the iso energetic KAM theorem and perpetual stability
of the Sun Jupiter Victoria problem 112
Appendix A. The Ellipse 117
Appendix B. Diophantine Estimates 121
B.I. Diophantine estimates for special quadratic numbers 121
B.2. Estimates on sp.fc( 5) 122
Appendix C. Interval Arithmetic 125
V
vi CONTENTS
Appendix D. A Guide to the Computer Programs 127
Bibliography 129
|
| adam_txt |
Contents
Chapter 1. Introduction 1
1.1. Quasi periodic solutions for the n body problem 1
1.2. A stability theorem for the Sun Jupiter Victoria system viewed as a
restricted, circular, planar three body problem 3
1.3. About the proof of the Sun Jupiter Victoria stability theorem 6
1.4. A short history of KAM stability estimates 8
1.5. A section by section summary 10
Chapter 2. Iso energetic KAM Theory 13
2.1. Notations 13
2.2. KAM tori 15
2.3. Newton scheme for finding iso energetic KAM tori 16
2.4. The KAM Map 27
2.5. Technical Tools 28
2.6. The KAM Norm Map 36
2.7. Iso energetic KAM Theorem 48
2.8. Iso energetic Lindstedt series 70
Chapter 3. The Restricted, Circular, Planar Three body Problem 75
3.1. The restricted three body problem 75
3.2. Delaunay action angle variables for the two body problem 75
3.3. The restricted, circular, planar three body problem viewed as
nearly integrable Hamiltonian system 84
3.4. The Sun Jupiter Asteroid problem 89
Chapter 4. KAM Stability of the Sun Jupiter Victoria Problem 95
4.1. Iso energetic Lindstedt series for the Sun Jupiter Asteroid problem
and choice of the initial approximate tori (u(0)±, a/0)±, w(0)±) 96
4.2. Evaluation of the input parameters of the KAM norm map associated
to the approximate tori (u*0^, «(0)±,w(0)±) 100
4.3. Iterations of the KAM map 108
4.4. Application of the iso energetic KAM theorem and perpetual stability
of the Sun Jupiter Victoria problem 112
Appendix A. The Ellipse 117
Appendix B. Diophantine Estimates 121
B.I. Diophantine estimates for special quadratic numbers 121
B.2. Estimates on sp.fc( 5) 122
Appendix C. Interval Arithmetic 125
V
vi CONTENTS
Appendix D. A Guide to the Computer Programs 127
Bibliography 129 |
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| author | Celletti, Alessandra Chierchia, Luigi 1957- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 521 - Celestial mechanics |
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| dewey-tens | 520 - Astronomy and allied sciences |
| discipline | Physik |
| discipline_str_mv | Physik |
| format | Book |
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| id | DE-604.BV022422893 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:26:18Z |
| indexdate | 2024-07-09T20:57:16Z |
| institution | BVB |
| isbn | 9780821841693 |
| language | English |
| lccn | 2007060667 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015631186 |
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| physical | VII, 134 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Celletti, Alessandra Verfasser aut KAM stability and celestial mechanics Alessandra Celletti ; Luigi Chierchia Providence, R.I. American Mathematical Society 2007 VII, 134 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 878 "May 2007, volume 187, number 878 (third of 4 numbers)." Includes bibliographical references Drie-deeltjes-systemen gtt Hemelmechanica gtt Mecânica celeste larpcal Storingsrekening gtt Three-body problem Celestial mechanics Perturbation (Mathematics) Himmelsmechanik (DE-588)4127484-2 gnd rswk-swf Dreikörperproblem (DE-588)4012974-3 gnd rswk-swf KAM-Theorie (DE-588)4329269-0 gnd rswk-swf Dreikörperproblem (DE-588)4012974-3 s Himmelsmechanik (DE-588)4127484-2 s KAM-Theorie (DE-588)4329269-0 s DE-604 Chierchia, Luigi 1957- Verfasser (DE-588)173917941 aut Memoirs of the American Mathematical Society 878 (DE-604)BV008000141 878 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015631186&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Celletti, Alessandra Chierchia, Luigi 1957- KAM stability and celestial mechanics Memoirs of the American Mathematical Society Drie-deeltjes-systemen gtt Hemelmechanica gtt Mecânica celeste larpcal Storingsrekening gtt Three-body problem Celestial mechanics Perturbation (Mathematics) Himmelsmechanik (DE-588)4127484-2 gnd Dreikörperproblem (DE-588)4012974-3 gnd KAM-Theorie (DE-588)4329269-0 gnd |
| subject_GND | (DE-588)4127484-2 (DE-588)4012974-3 (DE-588)4329269-0 |
| title | KAM stability and celestial mechanics |
| title_auth | KAM stability and celestial mechanics |
| title_exact_search | KAM stability and celestial mechanics |
| title_exact_search_txtP | KAM stability and celestial mechanics |
| title_full | KAM stability and celestial mechanics Alessandra Celletti ; Luigi Chierchia |
| title_fullStr | KAM stability and celestial mechanics Alessandra Celletti ; Luigi Chierchia |
| title_full_unstemmed | KAM stability and celestial mechanics Alessandra Celletti ; Luigi Chierchia |
| title_short | KAM stability and celestial mechanics |
| title_sort | kam stability and celestial mechanics |
| topic | Drie-deeltjes-systemen gtt Hemelmechanica gtt Mecânica celeste larpcal Storingsrekening gtt Three-body problem Celestial mechanics Perturbation (Mathematics) Himmelsmechanik (DE-588)4127484-2 gnd Dreikörperproblem (DE-588)4012974-3 gnd KAM-Theorie (DE-588)4329269-0 gnd |
| topic_facet | Drie-deeltjes-systemen Hemelmechanica Mecânica celeste Storingsrekening Three-body problem Celestial mechanics Perturbation (Mathematics) Himmelsmechanik Dreikörperproblem KAM-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015631186&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT cellettialessandra kamstabilityandcelestialmechanics AT chierchialuigi kamstabilityandcelestialmechanics |