Contents ix §8.5. Orientation, Notes and References 167 Chapter 9. Topological Linear Flows 169 §9.1. The Spectral Decomposition Theorem 170 §9.2. Selgrade’s Theorem 178 §9.3. The Morse Spectrum 184 §9.4. Lyapunov Exponents and the Morse Spectrum 192 §9.5. Application to Robust Linear Systems and Bilinear Control Systems 197 §9.6. Exercises 207 §9.7. Orientation, Notes and References 208 Chapter 10. Tools from Ergodic Theory 211 §10.1. Invariant Measures 211 §10.2. Birkhoff’s Ergodic Theorem 214 §10.3. Kingman’s Subadditive Ergodic Theorem 217 §10.4. Exercises 220 §10.5. Orientation, Notes and References 221 Chapter 11. Random Linear Dynamical Systems 223 §11.1. The Multiplicative Ergodic Theorem (MET) 224 §11.2. Some Background on Projections 233 §11.3. Singular Values, Exterior Powers, and the Goldsheid-Margulis Metric 237 §11.4. The Deterministic Multiplicative Ergodic Theorem 242 §11.5. The Furstenberg-Kesten Theorem and Proof of the MET in Discrete Time 252 §11.6. The Random Linear Oscillator 263 §11.7. Exercises 266 §11.8. Orientation, Notes and References 268 Bibliography 271 Index 279
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