| 1 | Introduction | 1 |
| 2 | Rigidity of hyperbolic manifolds | 11 |
| 3 | Three-manifolds which fiber over the circle | 41 |
| 4 | Quadratic maps and renormalization | 75 |
| 5 | Towers | 95 |
| 6 | Rigidity of towers | 105 |
| 7 | Fixed points of renormalization | 119 |
| 8 | Asymptotic structure in the Julia set | 135 |
| 9 | Geometric limits in dynamics | 151 |
| 10 | Conclusion | 175 |
| Appendix A. Quasiconformal maps and flows | 183 |
| Appendix B. Visual extension | 205 |
| Bibliography | 241 |
| Index | 251 |