Cover -- Title -- Copyright -- Contents -- Preface -- Introduction -- 1. Bibliography -- Part I. One Complex Variable -- Arithmetic of Unicritical Polynomial Maps -- 1. Introduction -- 2. Periodic orbits -- 3. Proofs -- 4. Postcritically finite maps -- 5. Bibliography -- Les racines des composantes hyperboliques de M sont des quarts d'entiers algébriques -- Dynamical cores of topological polynomials -- 1. Introduction and the main result -- 2. Preliminaries -- 3. Dynamical core -- 4. Bibliography -- The quadratic dynatomic curves are smooth and irreducible -- 1. Introduction -- 2. Dynatomic polynomials -- 3. Smoothness of the dynatomic curves -- 4. Irreducibility of the dynatomic curves -- 5. Bibliography -- Multicorns are not path connected -- 1. Introduction -- 2. Antiholomorphic and parabolic dynamics -- 3. Bifurcation along arcs and the fixed-point index -- 4. Parabolic perturbations -- 5. Parabolic trees and combinatorics -- 6. Non-pathwise connectivity -- 7. Further results -- 8. Bibliography -- Leading monomials of escape regions -- 1. Introduction -- 2. Statement of the results -- 3. Puiseux series dynamics statement -- 4. One-parameter families -- 5. Bibliography -- Limiting behavior of Julia sets of singularly perturbed rational maps -- 1. Introduction -- 2. Elementary mapping properties -- 3. Julia sets converging to the unit disk -- 4. The case n > 2 -- 5. Other c-values -- 6. Bibliography -- On (non-)local connectivity of some Julia sets -- 1. Local connectivity -- 2. Rational maps -- 3. Douady-Sullivan criterion -- 4. The case of infinitely satellite-renormalizable quadratic polynomials: a model -- 5. Bibliography -- Perturbations of weakly expanding critical orbits -- 1. Introduction -- 2. Polynomials -- 3. Rational functions -- 4. Part (a) of Theorem 3.6 -- 5. Part (b) of Theorem 3.6 -- 6. Bibliography.

Unmating of rational maps: Sufficient criteria and examples -- 1. Introduction -- 2. Moore's theorem -- 3. Mating of polynomials -- 4. Equators and hyperbolic rational maps -- 5. An example -- 6. A sufficient criterion for mating -- 7. Connections -- 8. Critical portraits -- 9. Unmating the map -- 10. Examples of unmatings -- 11. A mating not arising from a pseudo-equator -- 12. Open questions -- 13. Bibliography -- A framework toward understanding the characterization of holomorphic dynamics -- 1. Characterization -- 2. Obstruction -- 3. Review -- 4. Geometry -- 5. Geometrization -- 6. Appendix on Transcendental Functions by Tao Chen, Yunping Jiang, and Linda Keen -- 7. Bibliography -- Part II. One Real Variable -- Metric stability for random walks (with applications in renormalization theory) -- 1. Introduction -- 2. Expanding Markov maps, random walks, and their perturbations -- 3. Statements of results -- 4. Preliminaries -- 5. Stability of transience -- 6. Stability of recurrence -- 7. Stability of the multifractal spectrum -- 8. Applications to one-dimensional renormalization theory -- 9. Bibliography -- Milnor's conjecture on monotonicity of topological entropy: Results and questions -- 1. Motivation -- 2. Milnor's monotonicity of entropy conjecture -- 3. Idea of the proof -- 4. Open problems -- 5. Bibliography -- Entropy in dimension one -- 1. Introduction -- 2. Special case: Pisot numbers -- 3. Constructing interval maps: First steps -- 4. Second step: Constructing a map for λN -- 5. Powers and roots: Completion of proof of Theorem 1.3 -- 6. Maps of asterisks -- 7. Entropy in bounded degree -- 8. Traintracks -- 9. Splitting hairs -- 10. Dynamic extensions -- 11. Bipositive matrices -- 12. Tracks, doubletracks, zipping and a sketch of the proof of Theorem 1.11 -- 13. Supplementary notes (mostly by John Milnor) -- 14. Bibliography.

Part III. Several Complex Variables -- On Écalle-Hakim's theorems in holomorphic dynamics -- 1. Introduction -- 2. Notation -- 3. Preliminaries -- 4. Characteristic directions -- 5. Changes of coordinates -- 6. Existence of parabolic curves -- 7. Existence of attracting domains -- 8. Parabolic manifolds -- 9. Fatou coordinates -- 10. Fatou-Bieberbach domains -- 11. Bibliography -- Index theorems for meromorphic self-maps of the projective space -- 1. Introduction -- 2. The proof -- 3. Bibliography -- Dynamics of automorphisms of compact complex surfaces -- 1. Introduction -- 2. Hodge theory and automorphisms -- 3. Groups of automorphisms -- 4. Periodic curves, periodic points, and topological entropy -- 5. Invariant currents -- 6. Entire curves, stable manifolds, and laminarity -- 7. Fatou and Julia sets -- 8. The measure of maximal entropy and periodic points -- 9. Complements -- 10. Appendix: Classification of surfaces -- 11. Bibliography -- Bifurcation currents and equidistribution in parameter space -- 1. Prologue: normal families, currents and equidistribution -- 2. Bifurcation currents for families of rational mappings on P1 -- 3. Higher bifurcation currents and the bifurcation measure -- 4. Bifurcation currents for families of Möbius subgroups -- 5. Further settings, final remarks -- 6. Bibliography -- Part IV. Laminations and Foliations -- Entropy for hyperbolic Riemann surface laminations I -- 1. Introduction -- 2. Poincaré metric on laminations -- 3. Hyperbolic entropy for foliations -- 4. Entropy of harmonic measures -- 5. Bibliography -- Entropy for hyperbolic Riemann surface laminations II -- 1. Introduction -- 2. Local models for singular points -- 3. Poincaré metric on leaves -- 4. Finiteness of entropy: the strategy -- 5. Adapted transversals and their coverings -- 6. Finiteness of entropy: end of the proof -- 7. Bibliography.

Intersection theory for ergodic solenoids -- 1. Introduction -- 2. Measured solenoids and generalized currents -- 3. Homotopy of solenoids -- 4. Intersection theory of solenoids -- 5. Almost everywhere transversality -- 6. Intersection of analytic solenoids -- 7. Bibliography -- Invariants of four-manifolds with flows via cohomological field theory -- 1. Introduction -- 2. Asymptotic cycles and currents -- 3. Overview of cohomological quantum field theory: Donaldson-Witten invariants -- 4. Donaldson-Witten invariants for flows -- 5. Donaldson-Witten invariants for Kähler manifolds with flows -- 6. Survey on Seiberg-Witten invariants -- 7. Seiberg-Witten invariants for flows -- 8. A physical interpretation -- 9. Final remarks -- 10. Bibliography -- Color Plates -- Part V. Geometry and Algebra -- Two papers which changed my life: Milnor's seminal work on flat manifolds and bundles -- 1. Introduction -- 2. Gauss-Bonnet beginnings -- 3. The Milnor-Wood inequality -- 4. Maximal representations -- 5. Complete affine manifolds -- 6. Margulis spacetimes -- 7. Bibliography -- Milnor's problem on the growth of groups and its consequences -- 1. Introduction -- 2. Acknowledgments -- 3. Preliminary facts -- 4. The problem and the conjecture of Milnor -- 5. Relations between group growth and Riemannian geometry -- 6. Results about group growth obtained before 1981 -- 7. Growth and amenability -- 8. Polynomial growth -- 9. Intermediate growth: The construction -- 10. The gap conjecture -- 11. Intermediate growth: The upper and lower bounds -- 12. Asymptotic invariants of probabilistic and analytic nature and corresponding gap-type conjectures -- 13. Inverse orbit growth and examples with explicit growth -- 14. Miscellaneous -- 15. Bibliography -- Contributors -- Index.