Dynamical systems and linear algebra:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2014]
|
| Series: | Graduate studies in mathematics
volume 158 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis Seite 271 - 277 |
| Physical Description: | xv, 284 Seiten Diagramme |
| ISBN: | 9780821883198 |
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MARC
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Record in the Search Index
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| adam_text | Titel: Dynamical systems and linear algebra
Autor: Colonius, Fritz
Jahr: 2014
Contents Introduction Notation Part 1. Matrices and Linear Dynamical Systems Chapter 1. Autonomous Linear Differential and Difference Equations §1.1. Existence of Solutions §1.2. The Real Jordan Form §1.3. Solution Formulas §1.4. Lyapunov Exponents §1.5. The Discrete-Time Case: Linear Difference Equations §1.6. Exercises §1.7. Orientation, Notes and References Chapter 2. Linear Dynamical Systems in §2.1. Continuous-Time Dynamical Systems or Flows §2.2. Conjugacy of Linear Flows §2.3. Linear Dynamical Systems in Discrete Time §2.4. Exercises §2.5. Orientation, Notes and References Chapter 3. Chain Transitivity for Dynamical Systems §3.1. Limit Sets and Chain Transitivity §3.2. The Chain Recurrent Set xi xv 3 3 6 10 12 18 24 27 29 29 33 38 43 43 47 47 54
Contents viii §3.3. The Discrete-Time Case 59 §3.4. Exercises 63 §3.5. Orientation, Notes and References 65 Chapter 4. Linear Systems in Projective Space 67 §4.1. Linear Flows Induced in Projective Space 67 §4.2. Linear Difference Equations in Projective Space 75 §4.3. Exercises 78 §4.4. Orientation, Notes and References 78 Chapter 5. Linear Systems on Grassmannians 81 §5.1. Some Notions and Results from Multilinear Algebra 82 §5.2. Linear Systems on Grassmannians and Volume Growth 86 §5.3. Exercises 94 §5.4. Orientation, Notes and References 95 Part 2. Time-Varying Matrices and Linear Skew Product Systems Chapter 6. Lyapunov Exponents and Linear Skew Product Systems 99 §6.1. Existence of Solutions and Continuous Dependence 100 §6.2. Lyapunov Exponents 106 §6.3. Linear Skew Product Flows 113 §6.4. The Discrete-Time Case 118 §6.5. Exercises 121 §6.6. Orientation, Notes and References 123 Chapter 7. Periodic Linear Differential and Difference Equations 127 §7.1. Floquet Theory for Linear Difference Equations 128 §7.2. Floquet Theory for Linear Differential Equations 136 §7.3. The Mathieu Equation 144 §7.4. Exercises 151 §7.5. Orientation, Notes and References 153 Chapter 8. Morse Decompositions of Dynamical Systems 155 §8.1. Morse Decompositions 155 §8.2. Attractors 159 §8.3. Morse Decompositions, Attractors, and Chain Transitivity 164 §8.4. Exercises 166
Contents IX §8.5. Orientation, Notes and References 167 Chapter 9. Topological Linear Flows 169 §9.1. The Spectral Decomposition Theorem 170 §9.2. Selgrade’s Theorem 178 §9.3. The Morse Spectrum 184 §9.4. Lyapunov Exponents and the Morse Spectrum 192 §9.5. Application to Robust Linear Systems and Bilinear Control Systems 197 §9.6. Exercises 207 §9.7. Orientation, Notes and References 208 Chapter 10. Tools from Ergodic Theory 211 §10.1. Invariant Measures 211 §10.2. Birkhoff’s Ergodic Theorem 214 §10.3. Kingman’s Subadditive Ergodic Theorem 217 §10.4. Exercises 220 §10.5. Orientation, Notes and References 221 Chapter 11. Random Linear Dynamical Systems 223 §11.1. The Multiplicative Ergodic Theorem (MET) 224 §11.2. Some Background on Projections 233 §11.3. Singular Values, Exterior Powers, and the Goldsheid-Margulis Metric 237 §11.4. The Deterministic Multiplicative Ergodic Theorem 242 §11.5. The Furstenberg-Kesten Theorem and Proof of the MET in Discrete Time 252 §11.6. The Random Linear Oscillator 263 §11.7. Exercises 266 §11.8. Orientation, Notes and References 268 Bibliography 271 Index 279
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| any_adam_object | 1 |
| author | Colonius, Fritz Kliemann, Wolfgang 1949- |
| author_GND | (DE-588)1108566413 (DE-588)1073835537 |
| author_facet | Colonius, Fritz Kliemann, Wolfgang 1949- |
| author_role | aut aut |
| author_sort | Colonius, Fritz |
| author_variant | f c fc w k wk |
| building | Verbundindex |
| bvnumber | BV042161637 |
| classification_rvk | SK 350 SK 220 SK 810 |
| classification_tum | MAT 344f MAT 150f |
| ctrlnum | (OCoLC)891769897 (DE-599)GBV786557478 |
| dewey-full | 512.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5 |
| dewey-search | 512.5 |
| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV042161637 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:14:13Z |
| institution | BVB |
| isbn | 9780821883198 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027601273 |
| oclc_num | 891769897 |
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| owner_facet | DE-384 DE-29T DE-188 DE-703 DE-20 DE-634 DE-706 DE-11 DE-91G DE-BY-TUM |
| physical | xv, 284 Seiten Diagramme |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Colonius, Fritz Verfasser (DE-588)1108566413 aut Dynamical systems and linear algebra Fritz Colonius, Wolfgang Kliemann Providence, Rhode Island American Mathematical Society [2014] © 2014 xv, 284 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics volume 158 Literaturverzeichnis Seite 271 - 277 Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Topologische Dynamik (DE-588)4253345-4 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s Dynamisches System (DE-588)4013396-5 s Topologische Dynamik (DE-588)4253345-4 s DE-604 Kliemann, Wolfgang 1949- Verfasser (DE-588)1073835537 aut Erscheint auch als Online-Ausgabe 978-1-4704-1932-5 Graduate studies in mathematics volume 158 (DE-604)BV009739289 158 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027601273&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Colonius, Fritz Kliemann, Wolfgang 1949- Dynamical systems and linear algebra Graduate studies in mathematics Lineare Algebra (DE-588)4035811-2 gnd Topologische Dynamik (DE-588)4253345-4 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4253345-4 (DE-588)4013396-5 |
| title | Dynamical systems and linear algebra |
| title_auth | Dynamical systems and linear algebra |
| title_exact_search | Dynamical systems and linear algebra |
| title_full | Dynamical systems and linear algebra Fritz Colonius, Wolfgang Kliemann |
| title_fullStr | Dynamical systems and linear algebra Fritz Colonius, Wolfgang Kliemann |
| title_full_unstemmed | Dynamical systems and linear algebra Fritz Colonius, Wolfgang Kliemann |
| title_short | Dynamical systems and linear algebra |
| title_sort | dynamical systems and linear algebra |
| topic | Lineare Algebra (DE-588)4035811-2 gnd Topologische Dynamik (DE-588)4253345-4 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Lineare Algebra Topologische Dynamik Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027601273&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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