A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigororous verification on a model
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
Am. Math. Soc.
2006
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
844 = 179,3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | "Volume 179, number 844 (third of 5 numbers)." |
| Beschreibung: | VII, 141 S. graph. Darst. |
| ISBN: | 0821838245 |
Internformat
MARC
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| 100 | 1 | |a Delshams, Amadeu |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem |b heuristics and rigororous verification on a model |c Amadeu Delshams ; Rafael de la Llave ; Tere M. Seara |
| 264 | 1 | |a Providence, RI |b Am. Math. Soc. |c 2006 | |
| 300 | |a VII, 141 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v 844 = 179,3 | |
| 500 | |a "Volume 179, number 844 (third of 5 numbers)." | ||
| 650 | 4 | |a Nonholonomic dynamical systems | |
| 650 | 4 | |a Mechanics | |
| 650 | 4 | |a Differential equations | |
| 700 | 1 | |a De la Llave, Rafael |e Verfasser |4 aut | |
| 700 | 1 | |a Seara, Tere M. |e Verfasser |4 aut | |
| 810 | 2 | |a American Mathematical Society |t Memoirs of the American Mathematical Society |v 844 |w (DE-604)BV008000141 |9 844 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020036570&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-020036570 | ||
Datensatz im Suchindex
| _version_ | 1804142569629679616 |
|---|---|
| adam_text | Contents
Chapter 1. Introduction 1
Chapter 2. Heuristic discussion of the mechanism 7
2.1. Integrable systems, resonances, secondary tori 7
2.2. Heuristic description of the mechanism 9
Chapter 3. A simple model 15
Chapter 4. Statement of rigorous results 19
Chapter 5. Notation and definitions, resonances 25
Chapter 6. Geometric features of the unperturbed problem 27
Chapter 7. Persistence of the normally hyperbolic invariant manifold
and its stable and unstable manifolds 31
7.1. Explicit calculations of the perturbed invariant manifold 33
Chapter 8. The dynamics in Ae 37
8.1. A system of coordinates for A£ 39
8.2. Calculation of the reduced Hamiltonian 41
8.3. Isolating the resonances (resonant averaging) 43
8.3.1. The infinitesimal equations for averaging 44
8.3.2. The main averaging result, Theorem 8.9 46
8.3.3. Proof of Theorem 8.9 47
8.4. The non-resonant region (KAM theorem) 50
8.4.1. Some results on Diophantine approximation 52
8.4.2. The KAM Theorem for twist maps 55
8.5. Analyzing the resonances 58
8.5.1. Resonances of order 3 and higher 58
8.5.2. Preliminary analysis of resonances of order one or two 59
8.5.3. Primary and secondary tori near the first and second order
resonances 62
8.5.4. Proof of Theorem 8.30 and Corollary 8.31 68
8.5.5. Existence of stable and unstable manifolds of periodic orbits 82
Chapter 9. The scattering map 87
9.1. Some generalities about the scattering map 87
9.2. The scattering map in our model: definition and computation 89
V
vi CONTENTS
Chapter 10. Existence of transition chains 97
10.1. Transition chains 99
10.2. The scattering map and the transversality of heteroclinic
intersections 99
10.2.1. The non-resonant region and resonances of order 3 and
higher 103
10.2.2. Resonances of first order 104
10.2.3. Resonances of order 2 110
10.3. Existence of transition chains to objects of different topological
types 117
Chapter 11. Orbits shadowing the transition chains and proof of
theorem 4.1 121
Chapter 12. Conclusions and remarks 123
12.1. The role of secondary tori and the speed of diffusion 123
12.2. Comparison with [DLSOO] 123
12.3. Heuristics on the genericity properties of the hypothesis and
the phenomena 124
12.4. The hypothesis of polynomial perturbations 125
12.5. Involving other objects 126
12.6. Variational methods 127
12.7. Diffusion times 127
Chapter 13. An example 129
Acknowledgments 135
Bibliography 137
|
| any_adam_object | 1 |
| author | Delshams, Amadeu De la Llave, Rafael Seara, Tere M. |
| author_facet | Delshams, Amadeu De la Llave, Rafael Seara, Tere M. |
| author_role | aut aut aut |
| author_sort | Delshams, Amadeu |
| author_variant | a d ad l l r d llr llrd t m s tm tms |
| building | Verbundindex |
| bvnumber | BV025416729 |
| ctrlnum | (OCoLC)917365674 (DE-599)BVBBV025416729 |
| dewey-full | 510 515.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 515 - Analysis |
| dewey-raw | 510 515.39 |
| dewey-search | 510 515.39 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV025416729 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:33:51Z |
| institution | BVB |
| isbn | 0821838245 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020036570 |
| oclc_num | 917365674 |
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| owner | DE-11 DE-188 |
| owner_facet | DE-11 DE-188 |
| physical | VII, 141 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Am. Math. Soc. |
| record_format | marc |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Delshams, Amadeu Verfasser aut A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem heuristics and rigororous verification on a model Amadeu Delshams ; Rafael de la Llave ; Tere M. Seara Providence, RI Am. Math. Soc. 2006 VII, 141 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 844 = 179,3 "Volume 179, number 844 (third of 5 numbers)." Nonholonomic dynamical systems Mechanics Differential equations De la Llave, Rafael Verfasser aut Seara, Tere M. Verfasser aut American Mathematical Society Memoirs of the American Mathematical Society 844 (DE-604)BV008000141 844 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020036570&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Delshams, Amadeu De la Llave, Rafael Seara, Tere M. A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem heuristics and rigororous verification on a model Nonholonomic dynamical systems Mechanics Differential equations |
| title | A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem heuristics and rigororous verification on a model |
| title_auth | A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem heuristics and rigororous verification on a model |
| title_exact_search | A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem heuristics and rigororous verification on a model |
| title_full | A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem heuristics and rigororous verification on a model Amadeu Delshams ; Rafael de la Llave ; Tere M. Seara |
| title_fullStr | A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem heuristics and rigororous verification on a model Amadeu Delshams ; Rafael de la Llave ; Tere M. Seara |
| title_full_unstemmed | A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem heuristics and rigororous verification on a model Amadeu Delshams ; Rafael de la Llave ; Tere M. Seara |
| title_short | A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem |
| title_sort | a geometric mechanism for diffusion in hamiltonian systems overcoming the large gap problem heuristics and rigororous verification on a model |
| title_sub | heuristics and rigororous verification on a model |
| topic | Nonholonomic dynamical systems Mechanics Differential equations |
| topic_facet | Nonholonomic dynamical systems Mechanics Differential equations |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020036570&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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