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Dynamical Systems and Linear Algebra

Fritz Colonius Universität Augsburg, Augsburg, Germany
Wolfgang Kliemann Iowa State University, Ames, IA
Available Formats:
Hardcover ISBN: 978-0-8218-8319-8
Product Code: GSM/158
List Price: $72.00 MAA Member Price:$64.80
AMS Member Price: $57.60 Electronic ISBN: 978-1-4704-1932-5 Product Code: GSM/158.E List Price:$67.00
MAA Member Price: $60.30 AMS Member Price:$53.60
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $108.00 MAA Member Price:$97.20
AMS Member Price: $86.40 Click above image for expanded view Dynamical Systems and Linear Algebra Fritz Colonius Universität Augsburg, Augsburg, Germany Wolfgang Kliemann Iowa State University, Ames, IA Available Formats:  Hardcover ISBN: 978-0-8218-8319-8 Product Code: GSM/158  List Price:$72.00 MAA Member Price: $64.80 AMS Member Price:$57.60
 Electronic ISBN: 978-1-4704-1932-5 Product Code: GSM/158.E
 List Price: $67.00 MAA Member Price:$60.30 AMS Member Price: $53.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$108.00 MAA Member Price: $97.20 AMS Member Price:$86.40
• Book Details

Volume: 1582014; 284 pp
MSC: Primary 15; 34; 37; 39; 60; 93;

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.

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

• Part 1. Matrices and linear dynamical systems
• Chapter 1. Autonomous linear differential and difference equations
• Chapter 2. Linear dynamical systems in $\mathbb {R}^d$
• Chapter 3. Chain transitivity for dynamical systems
• Chapter 4. Linear systems in projective space
• Chapter 5. Linear systems on Grassmannians
• Part 2. Time-varying matrices and linear skew product systems
• Chapter 6. Lyapunov exponents and linear skew product systems
• Chapter 7. Periodic linear and differential and difference equations
• Chapter 8. Morse decompositions of dynamical systems
• Chapter 9. Topological linear flows
• Chapter 10. Tools from ergodic theory
• Chapter 11. Random linear dynamical systems

• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1582014; 284 pp
MSC: Primary 15; 34; 37; 39; 60; 93;

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.

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

• Part 1. Matrices and linear dynamical systems
• Chapter 1. Autonomous linear differential and difference equations
• Chapter 2. Linear dynamical systems in $\mathbb {R}^d$
• Chapter 3. Chain transitivity for dynamical systems
• Chapter 4. Linear systems in projective space
• Chapter 5. Linear systems on Grassmannians
• Part 2. Time-varying matrices and linear skew product systems
• Chapter 6. Lyapunov exponents and linear skew product systems
• Chapter 7. Periodic linear and differential and difference equations
• Chapter 8. Morse decompositions of dynamical systems
• Chapter 9. Topological linear flows
• Chapter 10. Tools from ergodic theory
• Chapter 11. Random linear dynamical systems
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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