Introduction to the Perturbation Theory of Hamiltonian Systems:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u. a.
Springer
2010
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| Series: | Springer Monographs in Mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 211 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9783642030277 9783642030284 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to the Perturbation Theory of Hamiltonian Systems |c Dmitry Treschev ; Oleg Zubelevich |
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Record in the Search Index
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| adam_text | CONTENTS HAMILTONIAN EQUATIONS 1 1.1 HAMILTONIAN SYSTEMS: GEOMETRIE
POINT OF VIEW 1 1.2 SYMPLEETIC MAPS 8 1.3 INCLUSION OF A DILIEOMORPHISM
INTO A FLOW 13 1.4 THE CLASSICAL PERTURBATION THEORY 18 INTRODUCTION TO
THE KAM THEORY 23 2.1 THE KOLMOGOROV THEOREM 23 2.2 A REDUCTION OF
THEOREMS 2.2-2.4 TO THE STANDARD VERSION 26 2.3 LOWER-DIMENSIONAL TORI
29 2.4 HYPERBOLIC TORI 35 2.5 HYPERBOLIC TORI: WEAK REDUCIBILITY 40 2.6
APPLICATIONS OF THE KAM THEORY 44 2.7 PERTURBATIONS OF A QUASI-PERIODIC
FLOW ON A TORUS 50 2.8 PROOF OF THE THEOREM ON THE REDUCTION OF A FLOW
53 SPLITTING OF ASYMPTOTIC MANIFOLDS 59 3.1 NORMAL COORDINATES 59 3.2
THE POINCARE-MELNIKOV METHOD: TRADITIONAL ASPECT 61 3.3 THE
POINCARE-MELNIKOV METHOD: MULTIDIMENSIONAL ASPECT 68 THE SEPARATRIX MAP
75 4.1 DEFINITION AND FORMULAS 75 4.1.1 TWO-DIMENSIONAL SYMPLEETIC MAP
75 4.1.2 HAMILTONIAN SYSTEM WITH ONE AND A HALF DEGREES OF FREEDOM 78
4.2 PROOF OF THEOREM 4.1 80 4.3 POINCARE-MELNIKOV INTEGRAL 84 4.4
HAMILTONIAN SYSTEM 88 4.5 SEPARATRIX MAP FOR A PENDULUM 90
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/99467998X DIGITALISIERT
DURCH X CONTENTS 4.6 SOME GENERALIZATIONS 91 5 WIDTH OF THE STOCHASTIC
LAYER 93 5. 1 DEFINITIONS AND RESULTS 93 5.2 THEOREMS ON THE STOCHASTIC
LAYER 96 5.3 STOCHASTIC LAYER FOR A PENDULUM 100 5.4 KAM THEORY AND THE
BIRKHOFF THEOREM 101 6 THE CONTINUOUS AVERAGING METHOD 107 6.1
DESCRIPTION OF THE METHOD 107 6.2 MAJORANTS 110 6.3 AN INCLUSION OF A
MAP INTO A FLOW 112 6.4 THE CASE OF ARBITRARY ALGEBRA X 116 6.5 FAST
PHASE AVERAGING 118 6.6 ANALYTIC PROPERTIES OF THE AVERAGING PROCEDURE
122 7 THE ANTI-INTEGRABLE LIMIT 131 7.1 PERTURBATION OF THE STANDARD MAP
131 7.2 A GENERAL CONSTRUCTION 133 7.3 FURTHER EXAMPLES 137 7.4
ANTI-INTEGRABLE LIMIT IN THE SEPARATRIX MAP 140 8 HILL S FORMULA 143 8.
1 GENERAL REMARKS 143 8.2 DISCRETE CASE 144 8.3 CONTINUOUS CASE 153 9
APPENDIX 163 9.1 DIOPHANTINE FREQUENCIES 163 9.2 CLOSURES OF ASYMPTOTIC
CURVES 168 9.3 INVARIANT TORI IN A NEIGHBORHOOD OF A RESONANCE 177 9.4
STABILITY ISLANDS IN SEPARATRIX LOBES 185 9.5 ELEMENTS OF ANALYSIS ON
SCALES 192 9.5.1 LOCALLY CONVEX SPACES 192 9.5.2 SCALES OF BANACH SPACES
194 9.5.3 OTHER EXAMPLES OF SCALES 196 9.5.
|
| any_adam_object | 1 |
| author | Treščev, Dmitrij V Zubelevič, Oleg |
| author_facet | Treščev, Dmitrij V Zubelevič, Oleg |
| author_role | aut aut |
| author_sort | Treščev, Dmitrij V |
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| building | Verbundindex |
| bvnumber | BV035844684 |
| callnumber-first | Q - Science |
| callnumber-label | QA614 |
| callnumber-raw | QA614.83 |
| callnumber-search | QA614.83 |
| callnumber-sort | QA 3614.83 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 810 |
| ctrlnum | (OCoLC)428028843 (DE-599)DNB99467998X |
| dewey-full | 515.392 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.392 |
| dewey-search | 515.392 |
| dewey-sort | 3515.392 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035844684 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:05:57Z |
| institution | BVB |
| isbn | 9783642030277 9783642030284 |
| language | English |
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| owner_facet | DE-384 DE-19 DE-BY-UBM DE-11 |
| physical | X, 211 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer Monographs in Mathematics |
| spelling | Treščev, Dmitrij V Verfasser aut Introduction to the Perturbation Theory of Hamiltonian Systems Dmitry Treschev ; Oleg Zubelevich Berlin u. a. Springer 2010 X, 211 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Springer Monographs in Mathematics Hamiltonian systems Perturbation (Mathematics) Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Störungstheorie (DE-588)4128420-3 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s Störungstheorie (DE-588)4128420-3 s DE-604 Zubelevič, Oleg Verfasser aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018702908&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Treščev, Dmitrij V Zubelevič, Oleg Introduction to the Perturbation Theory of Hamiltonian Systems Hamiltonian systems Perturbation (Mathematics) Hamiltonsches System (DE-588)4139943-2 gnd Störungstheorie (DE-588)4128420-3 gnd |
| subject_GND | (DE-588)4139943-2 (DE-588)4128420-3 |
| title | Introduction to the Perturbation Theory of Hamiltonian Systems |
| title_auth | Introduction to the Perturbation Theory of Hamiltonian Systems |
| title_exact_search | Introduction to the Perturbation Theory of Hamiltonian Systems |
| title_full | Introduction to the Perturbation Theory of Hamiltonian Systems Dmitry Treschev ; Oleg Zubelevich |
| title_fullStr | Introduction to the Perturbation Theory of Hamiltonian Systems Dmitry Treschev ; Oleg Zubelevich |
| title_full_unstemmed | Introduction to the Perturbation Theory of Hamiltonian Systems Dmitry Treschev ; Oleg Zubelevich |
| title_short | Introduction to the Perturbation Theory of Hamiltonian Systems |
| title_sort | introduction to the perturbation theory of hamiltonian systems |
| topic | Hamiltonian systems Perturbation (Mathematics) Hamiltonsches System (DE-588)4139943-2 gnd Störungstheorie (DE-588)4128420-3 gnd |
| topic_facet | Hamiltonian systems Perturbation (Mathematics) Hamiltonsches System Störungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018702908&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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