Measure and capacity of wandering domains in gevrey near-integrable exact symplectic systems:
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| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2019]
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
volume 257, number 1235 (fifth of 6 numbers) |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | vi, 110, 4 ungezählte Seiten |
| ISBN: | 9781470434922 |
Internformat
MARC
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| 100 | 1 | |a Lazzarini, Laurent |d 1971- |0 (DE-588)1179943430 |4 aut | |
| 245 | 1 | 0 | |a Measure and capacity of wandering domains in gevrey near-integrable exact symplectic systems |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2019] | |
| 264 | 4 | |c © 2019 | |
| 300 | |a vi, 110, 4 ungezählte Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 257, number 1235 (fifth of 6 numbers) | |
| 700 | 1 | |a Marco, Jean-Pierre |4 aut | |
| 700 | 1 | |a Sauzin, D. |d 1966- |0 (DE-588)1146415028 |4 aut | |
| 830 | 0 | |a Memoirs of the American Mathematical Society |v volume 257, number 1235 (fifth of 6 numbers) |w (DE-604)BV008000141 |9 1235 | |
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Datensatz im Suchindex
| _version_ | 1804179534766931968 |
|---|---|
| adam_text | Contents
Chapter 0. Introduction 1
Chapter 1. Presentation of the results 9
1.1. Perturbation theory for analytic or Gevrey near-integrable maps—
Theorem A 9
1.2. Wandering sets of near-integrable systems—Theorems B and C 12
1.3. Specific form of our examples and elliptic islands—Theorem D 15
1.4. Further comments 18
Chapter 2. Stability theory for Gevrey near-integrable maps 21
2.1. Embedding in a Hamiltonian flow — Theorem E 21
2.2. Proof of Theorem E in the Gevrey non-analytic case 22
2.2.0. Overview 22
2.2.1. First step: finding a generating function 23
2.2.2. Second step: constructing a Hamiltonian isotopy 26
2.2.3. Completion of the proof of Theorem E 28
2.3. Proof of Theorem A (Nekhoroshev Theorem for maps) 30
2.4. Proof of Theorem B (upper bounds for wandering sets) 32
Chapter 3. A quantitative KAM result—proof of Part (i) of Theorem D 33
3.1. Elliptic islands in A with a tuning parameter—Theorem F 33
3.2. Theorem F implies Part (i) of Theorem D 34
3.3. Overview of the proof of Theorem F 35
3.4. Preliminary study near a q-periodic point aq of Gn,^ 35
3.4.1. Localization 35
3.4.2. Local form of Gq 42
3.4.3. The Taylor expansion of Gq at aq 43
3.5. Normalizations 50
3.5.1. Notations and statements 51
Birkhoff normal form 52
Herman normal form 52
3.5.2. Proof of Proposition 3.16 53
3.5.3. Proof of Proposition 3.17 58
3.5.4. Proof of Proposition 3.18 63
3.6. The invariant curve theorem 64
3.7. Conclusion of the proof of Theorem F 65
Chapter 4. Coupling devices, multi-dimensional periodic domains, wandering
domains 69
4.1. Coupling devices 69
iii
IV
CONTENTS
4.2. Proof of Part (ii) of Theorem D (periodic domains in A71 1) 71
4.2.1. Overview of the method 71
4.2.2. A p-periodic polydisc for a near-integrable system of the form
o Fq in A 72
4.2.3. A ^-periodic polydisc for a near-integrable system G in An~2 73
4.2.4. Applying Corollary 4.2 75
4.3. Proof of Theorem C (lower bounds for wandering domains in An) 77
4.3.1. Overview of the proof 77
4.3.2. Standard maps with wandering discs in A — Proof of Proposition 4.6 77
4.3.3. Proof of Theorem C’ 78
Appendices 83
Appendix A. Algebraic operations in 0^ 83
Appendix B. Estimates on Gevrey maps 91
B.l. Reminder on Gevrey maps and their composition 91
B.2. A lemma on the flow of a Gevrey near-integrable Hamiltonian 92
B.3. Proof of Proposition 1.7 95
B.4. Gevrey bump fuctions 96
Appendix C. Generating functions for exact symplectic (7°° maps 99
Appendix D. Proof of Lemma 2.5 103
D.l. Set-up 103
D.2. Diffeomorphism property 103
D.3. Study of the inverse map 104
Acknowledgements 107
Bibliography 109
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:21:24Z |
| institution | BVB |
| isbn | 9781470434922 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030939912 |
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| physical | vi, 110, 4 ungezählte Seiten |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Lazzarini, Laurent 1971- (DE-588)1179943430 aut Measure and capacity of wandering domains in gevrey near-integrable exact symplectic systems Providence, Rhode Island American Mathematical Society [2019] © 2019 vi, 110, 4 ungezählte Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 257, number 1235 (fifth of 6 numbers) Marco, Jean-Pierre aut Sauzin, D. 1966- (DE-588)1146415028 aut Memoirs of the American Mathematical Society volume 257, number 1235 (fifth of 6 numbers) (DE-604)BV008000141 1235 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030939912&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lazzarini, Laurent 1971- Marco, Jean-Pierre Sauzin, D. 1966- Measure and capacity of wandering domains in gevrey near-integrable exact symplectic systems Memoirs of the American Mathematical Society |
| title | Measure and capacity of wandering domains in gevrey near-integrable exact symplectic systems |
| title_auth | Measure and capacity of wandering domains in gevrey near-integrable exact symplectic systems |
| title_exact_search | Measure and capacity of wandering domains in gevrey near-integrable exact symplectic systems |
| title_full | Measure and capacity of wandering domains in gevrey near-integrable exact symplectic systems |
| title_fullStr | Measure and capacity of wandering domains in gevrey near-integrable exact symplectic systems |
| title_full_unstemmed | Measure and capacity of wandering domains in gevrey near-integrable exact symplectic systems |
| title_short | Measure and capacity of wandering domains in gevrey near-integrable exact symplectic systems |
| title_sort | measure and capacity of wandering domains in gevrey near integrable exact symplectic systems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030939912&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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