Differentiable dynamics: an introduction to the orbit structure of diffeomorphisms
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, Mass.
M.I.T. Press
1971
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 282 S. Ill. |
| ISBN: | 0262140098 0262640112 |
Staff View
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| 100 | 1 | |a Nitecki, Zbigniew |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Differentiable dynamics |b an introduction to the orbit structure of diffeomorphisms |c Zbigniew Nitecki |
| 264 | 1 | |a Cambridge, Mass. |b M.I.T. Press |c 1971 | |
| 300 | |a XV, 282 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
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| adam_text | CONTENTS
PREFACE vii
INTRODUCTION: FLOWS AND DIFFEOMDRPHISMS 1
1. Time one maps 2
2. Cross sections and Suspensions 3
0. PRELIMINARIES 7
0.1 Function spaces 7
0.2 The Generic Viewpoint 18
0.3 A Quick Survey of Transversality Theory 25
1. THE CIRCLE 32
1.1 The Classical Theory 32
1.2 The Generic Theory 50
1.3 Expanding Maps 59
2. PERIODIC POINTS 68
2.0 Lipschitz Functions 68
2.1 Local Behavior of Periodic Points 71
2.2 Perturbations of Periodic Points 81
2.3 Morse Smale Systems 88
3. ANOSOV DIFFEOMORPHISMS 95
3*1 Hyperbolic Toral Automorphisms 96
3.2 The Anosov Stability Theorem 102
3«3 General Questions 111
4. THE HORSESHOE ll8
4.1 The Shift Automorphism 119
4.2 Definition of the Horseshoe 123
4.3 Formal Analysis of Q{f) 131
4.4 Linear Theory 138
4.5 Perturbations of f 141
4.6 Homoclinic Points 151
5 HYPERBOLIC SETS 159
5.1 Definition and the Stability Theorem 160
5.2 Stable Manifold Theory for a Point 164
5*3 Stable Manifold Theory for a Hyperbolic Set 179
vi Contents
6. THE n STABILITY THEOREM 1$9
6.1 Spectral Decomposition 190
6.2 Local Structure of Cl . 199
6.3 O Explosions 206
6.4 The No Cycle Property and Filtration 215
6.5 Global Stability 224
7. A SURVEY OF RECENT WORK 226
7.1 Stability Questions 226
7.2 Analysis of Invariant Sets 234
7.3 Other Areas 240
Appendix I ENDOMDRPHISMS OF THE CIRCLE 244
Appendix II THE KUPKA SMALE THEOREM 256
Appendix III PERIODIC POINTS OF TORAL AUTOMDRPHISMS 260
Appendix IV OPENNESS OF ANOSOV DIFFE0M3RPHISMS 262
BIBLIOGRAPHY 267
INDEX 279
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| any_adam_object | 1 |
| author | Nitecki, Zbigniew |
| author_facet | Nitecki, Zbigniew |
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| author_variant | z n zn |
| building | Verbundindex |
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| callnumber-first | Q - Science |
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| callnumber-search | QA613.65 |
| callnumber-sort | QA 3613.65 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 350 SK 810 |
| ctrlnum | (OCoLC)212088 (DE-599)BVBBV003012904 |
| dewey-full | 514/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.7 |
| dewey-search | 514/.7 |
| dewey-sort | 3514 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | Differentialdynamik gnd |
| genre_facet | Differentialdynamik |
| id | DE-604.BV003012904 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:52:14Z |
| institution | BVB |
| institution_GND | (DE-588)2179-9 |
| isbn | 0262140098 0262640112 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001886171 |
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| physical | XV, 282 S. Ill. |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | M.I.T. Press |
| record_format | marc |
| spelling | Nitecki, Zbigniew Verfasser aut Differentiable dynamics an introduction to the orbit structure of diffeomorphisms Zbigniew Nitecki Cambridge, Mass. M.I.T. Press 1971 XV, 282 S. Ill. txt rdacontent n rdamedia nc rdacarrier Diffeomorphisms Differentialtopologie (DE-588)4012255-4 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Differentialdynamik gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s DE-604 Differentialdynamik f Differentialtopologie (DE-588)4012255-4 s Massachusetts Institute of Technology Sonstige (DE-588)2179-9 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001886171&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nitecki, Zbigniew Differentiable dynamics an introduction to the orbit structure of diffeomorphisms Diffeomorphisms Differentialtopologie (DE-588)4012255-4 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| subject_GND | (DE-588)4012255-4 (DE-588)4137931-7 |
| title | Differentiable dynamics an introduction to the orbit structure of diffeomorphisms |
| title_auth | Differentiable dynamics an introduction to the orbit structure of diffeomorphisms |
| title_exact_search | Differentiable dynamics an introduction to the orbit structure of diffeomorphisms |
| title_full | Differentiable dynamics an introduction to the orbit structure of diffeomorphisms Zbigniew Nitecki |
| title_fullStr | Differentiable dynamics an introduction to the orbit structure of diffeomorphisms Zbigniew Nitecki |
| title_full_unstemmed | Differentiable dynamics an introduction to the orbit structure of diffeomorphisms Zbigniew Nitecki |
| title_short | Differentiable dynamics |
| title_sort | differentiable dynamics an introduction to the orbit structure of diffeomorphisms |
| title_sub | an introduction to the orbit structure of diffeomorphisms |
| topic | Diffeomorphisms Differentialtopologie (DE-588)4012255-4 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| topic_facet | Diffeomorphisms Differentialtopologie Differenzierbares dynamisches System Differentialdynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001886171&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT niteckizbigniew differentiabledynamicsanintroductiontotheorbitstructureofdiffeomorphisms AT massachusettsinstituteoftechnology differentiabledynamicsanintroductiontotheorbitstructureofdiffeomorphisms |