| 000 -LEADER |
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| fixed length control field |
nam a22 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
240213b xxu||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781470437299 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512.5 |
| Item number |
COL |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Colonius, Fritz |
| 245 ## - TITLE STATEMENT |
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| Title |
Dynamical systems and linear algebra |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc |
American Mathematical Society, |
| Date of publication, distribution, etc |
2014 |
| Place of publication, distribution, etc |
Providence : |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xv, 284 p. : |
| Other physical details |
ill., |
| Dimensions |
24 cm. |
| 365 ## - TRADE PRICE |
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| Price amount |
1405.00 |
| Price type code |
₹ |
| Unit of pricing |
01 |
| 490 ## - SERIES STATEMENT |
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| Series statement |
Graduate studies in mathematics ; |
| Volume number/sequential designation |
v.158 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
This book provides n introduction to the interplay between linear algebra and dynamical systems in continuous time and in discrete time. It first reviews the autonomous case for one matrix A via induced dynamical systems in ℝᵈ and on Grassmannian manifolds. Then the main nonautonomous approaches are presented for which the time dependency of A(t) is given via skew-product flows using periodicity, or topological (chain recurrence) or ergodic properties (invariant measures). The authors develop generalizations of (real parts of) eigenvalues and eigenspaces as a starting point for a linear algebra for classes of time-varying linear systems, namely periodic, random, and perturbed (or controlled) systems. The book presents for the first time in one volume a unified approach via Lyapunov exponents to detailed proofs of Floquet theory, of the properties of the Morse spectrum, and of the multiplicative ergodic theorem for products of random matrices. The main tools, chain recurrence and Morse decompositions, as well as classical ergodic theory are introduced in a way that makes the entire material accessible for beginning graduate students. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Topological dynamics |
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| Topical term or geographic name as entry element |
Vector bundle |
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| Topical term or geographic name as entry element |
Attractor |
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| Topical term or geographic name as entry element |
Chain components |
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| Topical term or geographic name as entry element |
Eigenvalues |
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| Topical term or geographic name as entry element |
Floquet theory |
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| Topical term or geographic name as entry element |
Algebras Linear |
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| Topical term or geographic name as entry element |
Matrix theory |
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| Topical term or geographic name as entry element |
Jordan block |
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| Topical term or geographic name as entry element |
Lyapunov spaces |
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| Topical term or geographic name as entry element |
Metric dynamical system |
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| Topical term or geographic name as entry element |
Subadditive ergodic theorem |
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| Topical term or geographic name as entry element |
Multiplicative Ergodic Theorem |
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| Topical term or geographic name as entry element |
Periodic matrix |
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| Topical term or geographic name as entry element |
Probability theory |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Kliemann, Wolfgang |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
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| Item type |
Books |