Contents xi Exercises 12.1 555 12.2. Classification of Periodic Points 555 Exercises 12.2 566 12.3. Stable Manifolds 567 Exercises 12.3 575 12.4. Hyperbolic Toral Automorphisms 575 Exercises 12.4 580 12.5. Applications 580 Exercises 12.5 594 12.6. Theory and Proofs 595 Chapter 13. Invariant Sets for Higher Dimensional Maps 597 13.1. Geometric Horseshoe 598 Exercises 13.1 611 13.2. Symbolic Dynamics 612 Exercises 13.2 632 13.3. Homoclinic Points and Horseshoes 636 Exercises 13.3 639 13.4. Attractors 639 Exercises 13.4 649 13.5. Lyapunov Exponents 650 Exercises 13.5 661 13.6. Applications 662 13.7. Theory and Proofs 664 Chapter 14. Fractals 669 14.1. Box Dimension 670 Exercises 14.1 679 14.2. Dimension of Orbits 680 Exercises 14.2 684 14.3. Iterated-Function Systems 684 Exercises 14.3 696 14.4. Theory and Proofs 697 Appendix A. Background and Terminology 705 A.1. Calculus Background and Notation 705 A.2. Analysis and Topology Terminology 707 A.3. Matrix Algebra 713 Appendix B. Generic Properties 717 Bibliography 721 Index 727
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