viii Contents §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
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