x Contents Exercises 9.4 390 9.5. Bifurcation of Periodic Points 391 Exercises 9.5 404 9.6. Conjugacy 406 Exercises 9.6 411 9.7. Applications 412 Exercises 9.7 416 9.8. Theory and Proofs 417 Chapter 10. Itineraries for One-Dimensional Maps 423 10.1. Periodic Points from Transition Graphs 424 Exercises 10.1 435 10.2. Topological Transitivity 437 Exercises 10.2 441 10.3. Sequences of Symbols 442 Exercises 10.3 451 10.4. Sensitive Dependence on Initial Conditions 451 Exercises 10.4 454 10.5. Cantor Sets 455 Exercises 10.5 463 10.6. Piecewise Expanding Maps and Subshifts 464 Exercises 10.6 473 10.7. Applications 475 Exercises 10.7 478 10.8. Theory and Proofs 479 Chapter 11. Invariant Sets for One-Dimensional Maps 487 11.1. Limit Sets 487 Exercises 11.1 490 11.2. Chaotic Attractors 490 Exercises 11.2 505 11.3. Lyapunov Exponents 507 Exercises 11.3 513 11.4. Invariant Measures 514 Exercises 11.4 533 11.5. Applications 534 11.6. Theory and Proofs 537 Chapter 12. Periodic Points of Higher Dimensional Maps 541 12.1. Dynamics of Linear Maps 541

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