**Graduate Studies in Mathematics**

Volume: 158;
2014;
284 pp;
Hardcover

MSC: Primary 15; 34; 37; 39; 60; 93;

**Print ISBN: 978-0-8218-8319-8
Product Code: GSM/158**

List Price: $72.00

AMS Member Price: $57.60

MAA Member Price: $64.80

**Electronic ISBN: 978-1-4704-1932-5
Product Code: GSM/158.E**

List Price: $67.00

AMS Member Price: $53.60

MAA Member Price: $60.30

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#### Supplemental Materials

# Dynamical Systems and Linear Algebra

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*Fritz Colonius; Wolfgang Kliemann*

This book provides an 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 \(\mathbb{R}^d\) 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.

#### Readership

Graduate students and research mathematicians interested in matrices and random dynamical systems.

#### Table of Contents

# Table of Contents

## Dynamical Systems and Linear Algebra

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Introduction xi12 free
- Notation xv16 free
- Part 1. Matrices and linear dynamical systems 118 free
- Chapter 1. Autonomous linear differential and difference equations 320
- Chapter 2. Linear dynamical systems in ℝ^{𝕕} 2946
- Chapter 3. Chain transitivity for dynamical systems 4764
- Chapter 4. Linear systems in projective space 6784
- Chapter 5. Linear systems on Grassmannians 8198
- Part 2. Time-varying matrices and linear skew product systems 97114
- Chapter 6. Lyapunov exponents and linear skew product systems 99116
- Chapter 7. Periodic linear and differential and difference equations 127144
- Chapter 8. Morse decompositions of dynamical systems 155172
- Chapter 9. Topological linear flows 169186
- Chapter 10. Tools from ergodic theory 211228
- Chapter 11. Random linear dynamical systems 223240
- Bibliography 271288
- Index 279296 free
- Back Cover Back Cover1302