Frontiers in complex dynamics: in celebration of John Milnor's 80th birthday
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| Format: | Book |
| Language: | English |
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Princeton, New Jersey ; Oxfordshire, England
Princeton University Press
2014
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| Series: | Princeton mathematical series
51 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XII, 787, 24 Seiten Illustrationen |
| ISBN: | 9780691159294 |
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| 245 | 1 | 0 | |a Frontiers in complex dynamics |b in celebration of John Milnor's 80th birthday |c edited by Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland |
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| adam_text | Titel: Frontiers in complex dynamics
Autor: Bonifant, Araceli
Jahr: 2014
Contents Preface xi Introduction 1 1. Bibliography 8 Part I. One Complex Variable 13 J. Milnor: Arithmetic of Unicritical Polynomial Maps 15 1. Introduction 15 2. Periodic orbits 15 3. Proofs 18 4. Postcritically finite maps 20 5. Bibliography 23 T. BOUSCH: Les racines des composantes hyperboliques de A4 sont des quarts d entiers algébriques 25 A. Blokh, L. Oversteegen, R. Ptacek, and V. Timorin: Dynamical cores of topological polynomials 27 1. Introduction and the main result 27 2. Preliminaries 29 3. Dynamical core 35 4. Bibliography 47 X. Buff and Tan Lei: The quadratic dynatomic curves are smooth and irreducible 49 1. Introduction 49 2. Dynatomic polynomials 50 3. Smoothness of the dynatomic curves 53 4. Irreducibility of the dynatomic curves 61 5. Bibliography 71 J. H. Hubbard and D. Schleicher: Multicoms are not path connected 73 1. Introduction 73 2. Antiholomorphic and parabolic dynamics 77 3. Bifurcation along arcs and the fixed-point index 80 4. Parabolic perturbations 85 5. Parabolic trees and combinatorics 89 6. Non-pathwise connectivity 95 7. Further results 98 8. Bibliography 101
VI CONTENTS J. KIWI: Leading monomials of escape regions 103 1. Introduction 103 2. Statement of the results 104 3. Puiseux series dynamics statement 106 4. One-parameter families 108 5. Bibliography 118 R. L. DevanEY: Limiting behavior of Julia sets of singularly perturbed rational maps 121 1. Introduction 121 2. Elementary mapping properties 123 3. Julia sets converging to the unit disk 126 4. The case n 2 128 5. Other c-values 131 6. Bibliography 133 A. DEZOTTI and P. Roesch: On (non-)local connectivity of some Julia sets 135 1. Local connectivity 136 2. Rational maps 141 3. Douady-Sullivan criterion 143 4. The case of infinitely satellite-renormalizable quadratic polynomials: a model 150 5. Bibliography 161 G. Levin: Perturbations of weakly expanding critical orbits 163 1. Introduction 163 2. Polynomials 167 3. Rational functions 176 4. Part (a) of Theorem 3.6 182 5. Part (b) of Theorem 3.6 189 6. Bibliography 195 D. Meyer: Unmating of rational maps: Sufficient criteria and examples 197 1. Introduction 197 2. Moore s theorem 199 3. Mating of polynomials 201 4. Equators and hyperbolic rational maps 204 5. An example 209 6. A sufficient criterion for mating 211 7. Connections 216 8. Critical portraits 220 9. Unmating the map 221 10. Examples of unmatings 224 11. A mating not arising from a pseudo-equator 228 12. Open questions 232 13. Bibliography 232
CONTENTS vii Y. JlANG: A framework toward understanding the characterization of holomorphic dynamics 235 1. Characterization 235 2. Obstruction 237 3. Review 237 4. Geometry 242 5. Geometrization 248 6. Appendix on Transcendental Functions by Tao Chen, Yunping Jiang, and Linda Keen 252 7. Bibliography 254 Part II. One Real Variable 259 C. G. Moreira and D. Smania: Metric stability for random walks (with applications in renormalization theory) 261 1. Introduction 261 2. Expanding Markov maps, random walks, and their perturbations 265 3. Statements of results 269 4. Preliminaries 272 5. Stability of transience 276 6. Stability of recurrence 288 7. Stability of the multifractal spectrum 296 8. Applications to one-dimensional renormalization theory 312 9. Bibliography 321 S. van STRIEN: Milnor s conjecture on monotonicity of topological entropy: Results and questions 323 1. Motivation 323 2. Milnor s monotonicity of entropy conjecture 324 3. Idea of the proof 326 4. Open problems 331 5. Bibliography 334 W. P. Thurston: Entropy in dimension one 339 1. Introduction 339 2. Special case: Pisot numbers 346 3. Constructing interval maps: First steps 351 4. Second step: Constructing a map for N 355 5. Powers and roots: Completion of proof of Theorem 1.3 355 6. Maps of asterisks 358 7. Entropy in bounded degree 359 8. Traintracks 365 9. Splitting hairs 367 10. Dynamic extensions 369 11. Bipositive matrices 370 12. Tracks, doubletracks, zipping and a sketch of the proof of Theorem 1.11 374 13. Supplementary notes (mostly by John Milnor) 376 14. Bibliography 383
CONTENTS viii Part III. Several Complex Variables 385 M. Arizzi and J. Raissv: On Écalle-Hakim s theorems in holomorphic dynamics 387 1. Introduction 387 2. Notation 389 3. Preliminaries 389 4. Characteristic directions 390 5. Changes of coordinates 397 6. Existence of parabolic curves 407 7. Existence of attracting domains 421 8. Parabolic manifolds 423 9. Fatou coordinates 439 10. Fatou-Bieberbach domains 444 11. Bibliography 447 M. Abate: Index theorems for meromorphic self-maps of the projective space 451 1. Introduction 451 2. The proof 453 3. Bibliography 460 S. CANTAT: Dynamics of automorphisms of compact complex surfaces 463 1. Introduction 463 2. Hodge theory and automorphisms 466 3. Groups of automorphisms 476 4. Periodic curves, periodic points, and topological entropy 478 5. Invariant currents 485 6. Entire curves, stable manifolds, and laminarity 489 7. Fatou and Julia sets 498 8. The measure of maximal entropy and periodic points 502 9. Complements 505 10. Appendix: Classification of surfaces 507 11. Bibliography 509 R. Dujardin: Bifurcation currents and equidistribution in parameter space 515 1. Prologue: normal families, currents and equidistribution 518 2. Bifurcation currents for families of rational mappings on P 1 524 3. Higher bifurcation currents and the bifurcation measure 534 4. Bifurcation currents for families of Möbius subgroups 547 5. Further settings, final remarks 557 6. Bibliography 559 Part IV. Laminations and Foliations 567 T. -C. Dinh, V.-A. Nguyên and N. Sibony: Entropy for hyperbolic Riemann surface laminations I 569 1. Introduction 569
CONTENTS ix 2. Poincaré metric on laminations 571 3. Hyperbolic entropy for foliations 578 4. Entropy of harmonic measures 585 5. Bibliography 591 T.-C. Dinh, V.-A. Nguyen and N. Sibony: Entropy for hyperbolic Riemann surface laminations II 593 1. Introduction 593 2. Local models for singular points 595 3. Poincaré metric on leaves 604 4. Finiteness of entropy: the strategy 611 5. Adapted transversals and their coverings 614 6. Finiteness of entropy: end of the proof 619 7. Bibliography 621 V. MUNOZ and R. Pérez-Marco: Intersection theory for ergodic solenoids 623 1. Introduction 623 2. Measured solenoids and generalized currents 624 3. Homotopy of solenoids 627 4. Intersection theory of solenoids 630 5. Almost everywhere transversality 638 6. Intersection of analytic solenoids 641 7. Bibliography 644 H. Garcîa-Compeà n, R. Santos-Silva and a. Verjovsky: Invariants of four-manifolds with flows via cohomological field theory 645 1. Introduction 645 2. Asymptotic cycles and currents 647 3. Overview of cohomological quantum field theory: Donaldson- Witten invariants 650 4. Donaldson-Witten invariants for flows 653 5. Donaldson-Witten invariants for Kà hler manifolds with flows 659 6. Survey on Seiberg-Witten invariants 667 7. Seiberg-Witten invariants for flows 669 8. A physical interpretation 672 9. Final remarks 673 10. Bibliography 674 Color Plates C-l Part V. Geometry and Algebra 677 W. Goldman: Two papers which changed my life: Milnor s seminal work on flat manifolds and bundles 679 1. Introduction 679 2. Gauss-Bonnet beginnings 679 3. The Milnor-Wood inequality 682 4. Maximal representations 684
X CONTENTS 5. Complete affine manifolds 687 6. Margulis spacetimes 691 7. Bibliography 699 R. Grigorchuk: Milnor s problem on the growth of groups and its consequences 705 1. Introduction 705 2. Acknowledgments 709 3. Preliminary facts 709 4. The problem and the conjecture of Milnor 713 5. Relations between group growth and Riemannian geometry 715 6. Results about group growth obtained before 1981 717 7. Growth and amenability 719 8. Polynomial growth 722 9. Intermediate growth: The construction 726 10. The gap conjecture 734 11. Intermediate growth: The upper and lower bounds 738 12. Asymptotic invariants of probabilistic and analytic nature and corresponding gap-type conjectures 743 13. Inverse orbit growth and examples with explicit growth 750 14. Miscellaneous 753 15. Bibliography 758 Contributors 775 Index 779
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| spelling | Frontiers in complex dynamics in celebration of John Milnor's 80th birthday edited by Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland Princeton, New Jersey ; Oxfordshire, England Princeton University Press 2014 XII, 787, 24 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Princeton mathematical series 51 Literaturangaben Dynamisches System (DE-588)4013396-5 gnd rswk-swf Komplexes System (DE-588)4114261-5 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content (DE-588)4016928-5 Festschrift gnd-content Dynamisches System (DE-588)4013396-5 s Komplexes System (DE-588)4114261-5 s 1\p DE-604 Bonifant, Araceli 1963- (DE-588)1063011825 edt Milnor, John Willard 1931- (DE-588)119533073 hnr Princeton mathematical series 51 (DE-604)BV000019035 51 DE-601 pdf/application http://www.gbv.de/dms/bowker/toc/9780691159294.pdf Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027556604&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
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| title | Frontiers in complex dynamics in celebration of John Milnor's 80th birthday |
| title_auth | Frontiers in complex dynamics in celebration of John Milnor's 80th birthday |
| title_exact_search | Frontiers in complex dynamics in celebration of John Milnor's 80th birthday |
| title_full | Frontiers in complex dynamics in celebration of John Milnor's 80th birthday edited by Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland |
| title_fullStr | Frontiers in complex dynamics in celebration of John Milnor's 80th birthday edited by Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland |
| title_full_unstemmed | Frontiers in complex dynamics in celebration of John Milnor's 80th birthday edited by Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland |
| title_short | Frontiers in complex dynamics |
| title_sort | frontiers in complex dynamics in celebration of john milnor s 80th birthday |
| title_sub | in celebration of John Milnor's 80th birthday |
| topic | Dynamisches System (DE-588)4013396-5 gnd Komplexes System (DE-588)4114261-5 gnd |
| topic_facet | Dynamisches System Komplexes System Aufsatzsammlung Festschrift |
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