Hardcover ISBN:  9780821883198 
Product Code:  GSM/158 
List Price:  $72.00 
MAA Member Price:  $64.80 
AMS Member Price:  $57.60 
Electronic ISBN:  9781470419325 
Product Code:  GSM/158.E 
List Price:  $67.00 
MAA Member Price:  $60.30 
AMS Member Price:  $53.60 

Book DetailsGraduate Studies in MathematicsVolume: 158; 2014; 284 ppMSC: 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 skewproduct 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 timevarying 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.ReadershipGraduate students and research mathematicians interested in matrices and random dynamical systems.

Table of Contents

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. Timevarying 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


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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 skewproduct 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 timevarying 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. Timevarying 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