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On the geometry and dynamics of diffeomorphisms of surfaces
Author(s):
William P.
Thurston
Journal:
Bull. Amer. Math. Soc.
19
(1988),
417-431.
MSC (1985):
Primary 58F15
MathSciNet review:
956596
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References:
- [Anosov] D. V. Anosov, Geodesic flows on closed Riemannian manifolds with negative curvature, Trudy Mat. Inst. Steklov. 90 (1967); English transl., Proc. Steklov. Inst. Math. 90 (1969). MR 224110
- [ArnYoc] P. Arnoux and J. C. Yoccoz, Construction de diffeomorphismes pseudo-Anosov, C. R. Acad. Sci. Paris Ser. I Math. 292 (1981), 75-78. MR 610152
- [Bers1] L. Bers, An extremal problem for quasiconformal mapping and a theorem by Thurston, Acta Math. 141 (1978), 73-98. MR 477161
- [Bers2] L. Bers, On boundaries of Teichmüller spaces and Kleinian groups. I, Ann. of Math. (2) 91 (1970), 570-600. MR 297992
- [Bers3] L. Bers, On iterates of hyperbolic transformations of Teichmüller space, Amer. J. Math. 105 (1983), 1-11. MR 692104
- [BirKid] J. Birman and M. Kidwell, Fixed points of pseudo-Anosov diffeomorphisms of surfaces, Adv. in Math. 46 (1982), 217-220. MR 679909
- [Bonahon1] F. Bonahon, Cobordism of automorphisms of surfaces, Ann. Sci. École Norm. Sup. 16 (1983), 237-270. MR 732345
- [Bonahon2] F. Bonahon, Bouts des variétés hyperboliques de dimension 3, Ann. of Math. (2) 124 (1986), 71-158. MR 847953
- [CasBlei] A. J. Casson, Notes by S. A. Bleiler, Automorphisms of surfaces, after Nielsen and Thurston, Preprint (1982). MR 964685
- [CasLong] A. J. Casson and D. D. Long, Algorithmic compression of surface automorphisms, preprint. MR 799268
- [CulMor] M. Culler and J. W. Morgan, Group actions on R-trees, Proc. London Math. Soc. (to appear). MR 907233
- [CulShal1] M. Culler and P. Shalen, Varieties of group representation and splittings of 3-manifolds, Ann. of Math. (2) 117 (1983), 43-45. MR 683804
- [CulShal2] M. Culler and P. Shalen, Bounded, separating surfaces in knot manifolds, Invent. Math. 75 (1984), 537-545. MR 735339
- [FatLau] A. Fathi and F. Laudenbach, Diffeomorphismes pseudo-Anosov et decomposition de Heegaard, C. R. Acad. Sci. Paris Ser. A-B 291 (1980), A423-A425. MR 596088
- [Fathi1] A. Fathi, The Poisson bracket on the space of measured foliations on a surface, Duke J. Math.
- [Fathi2] A. Fathi, Dehn twists and pseudo-Anosov diffeomorphisms, preprint. MR 862715
- [FLP] A. Fathi, F. Laudenbach and V. Poenaru et al., Travaux de Thurston sur les surfaces, Astérisque 66-67 (1979), 1-284. MR 568308
- [Fried1] D. Fried, Transitive Anosov flows and pseudo-Anosov maps, Topology 22 (1983), 299-303. MR 710103
- [Fried2] D. Fried, Flow equivalence, hyperbolic systems and a new zeta function for flows, Comment. Math. Helv. 57 (1982), 237-259. MR 684116
- [Fried3] D. Fried, Growth rate of surface homeomorphisms and flow equivalence, preprint. MR 829857
- [GerKat] M. Gerber and A. Katok, Smooth models of Thurston's pseudo-Anosov maps, Ann. Sci. École Norm. Sup. 15 (1982), 173-204. MR 672479
- [Gilman1] J. Gilman, On the Nielsen type and the classification for the mapping-class group, Adv. in Math. 40 (1981), 68-96. MR 616161
- [Gilman2] J. Gilman, Determining Thurston classes using Nielsen types, Trans. Amer. Math. Soc. 272 (1982), 669-675. MR 662059
- [Gard] F. P. Gardiner, Teichmüller theory and quadratic differentials, Wiley, New York, 1987. MR 903027
- [Handel1] M. Handel, Global shadowing of pseudo-Anosov homeomorphisms, Ergodic Theory and Dynamical Systems (to appear). MR 805836
- [Handel2] M. Handel, Entropy and semi-conjugacy in dimension 2, Ergodic Theory and Dynamical Systems (to appear). MR 980798
- [HanTh] M. Handel and W. P. Thurston, Anosov flows on new three-manifolds, Invent. Math. MR 577356
- [HanTh] M. Handel and W. P. Thurston, New proofs of some results of Nielsen, Adv. in Math. 56 (1985), 173-191. MR 788938
- [HatTh] A. Hatcher and W. Thurston, Incompressible surfaces in 2-bridge knot complements, Invent. Math. 79 (1985), 225-246. MR 778125
- [Harer] J. Harer, Stability of the homology of the mapping class groups of orientable surfaces, Ann. of Math. (2) 121 (1985), 215-249. MR 786348
- [HubMas] J. Hubbard and H. Masur, Quadratic differentials and foliations, Acta Math. 142 (1979), 221-274. MR 523212
- [Kerckhoff1] S. P. Kerckhoff, The asymptotic geometry of Teichmüller space, Topology 19 (1980), 23-41. MR 559474
- [Kerckhoff2] S. P. Kerckhoff, The Nielsen realization problem, Ann. of Math. (2) 117 (1983), 235-265. MR 690845
- [Kerckhoff3] S. P. Kerckhoff, Earthquakes are analytic, Comment. Math. Helv. 60 (1985), 17-30. MR 787659
- [KMS] S. Kerckhoff, H. Masur and J. Smillie, Ergodicity of billiard flows and quadratic differentials, Ann. of Math. (2) 124 (1986), 293-311. MR 855297
- [Kra] I. Kra, On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces, Acta Math. 146 (1981), 231-270. MR 611385
- [Masur1] H. Masur, Interval exchange transformations and measured foliations, Ann. of Math. (2) 115 (1982), 169-200. MR 644018
- [Masur2] H. Masur, Ergodic actions of the mapping class group, Proc. Amer. Math. Soc. 94 (1985), 455-459. MR 787893
- [Masur3] H. Masur, Two boundaries of Teichmüller space, Duke Math. J. 49 (1982), 183-190. MR 650376
- [Miller] R. T. Miller, Geodesic laminations from Nielsen's viewpoint, Adv. in Math. 45 (1982), 189-212. MR 664623
- [MorShal1] J. W. Morgan and P. Shalen, Valuations, trees, and degenerations of hyperbolic structures. I, Ann. of Math. (2) 120 (1984), 401-476. MR 769158
- [MorShal2] J. W. Morgan and P. Shalen, Degenerations of hyperbolic structures. II: measured laminations, trees and 3-manifolds, Ann. of Math. (2) 127 (1988), 403-456. MR 932305
- [MorShal3] J. W. Morgan and P. Shalen, Degenerations of hyperbolic structures. III, Ann. of Math. (2) 127 (1988). MR 932305
- [Mosher0] L. Mosher, Pseudo-Anosovs on punctured surfaces, Princeton thesis, 1983.
- [Mosherl] L. Mosher, The classification of pseudo-Anosovs, Proceedings of Conference on Hyperbolic Geometry in Durham, Cambridge Univ. Press. MR 903858
- [Mosher2] L. Mosher, Topological invariants of measured foliations, Preprint, 1988.
- [Nielsen1] J. Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen. I, Acta Math. 50 (1927), 189-358. MR 1555256
- [Nielsen2] J. Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen. II, Acta Math. 53 (1929), 1-76. MR 1555290
- [Nielsen3] J. Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen. III, Acta Math. 58 (1932), 87-167. MR 1555345
- [Oertel] U. Oertel, Measured laminations in 3-manifolds, Trans. Amer. Math. Soc. 305 (1988), 531-573. MR 924769
- [Pap1] A. Papadopoulos, Diffeomorphismes pseudo-Anosov et automorphismes symplectiques de l'homologie, Ann. Sci. École Norm. Sup. 15 (1982), 543-546. MR 690652
- [Pap2] A. Papadopoulos, L'extension du flot de Fenchel-Nielsen au bord de Thurston de l'espace de Teichmüller, C. R. Acad. Sci. Paris 302 (1986), 325-327. MR 838585
- [Pap3] A. Papadopoulos, Geometrie intersection functions and hamiltonian flows on the space of measured foliations on a surface, Pacific J. Math. 124 (1986), 375-402. MR 856170
- [Pap4] A. Papadopoulos, Sur le bord de Thurston de l'espace de Teichmüller d'une surface non compacte, Math. Ann. (1988). MR 967017
- [Pap5] A. Papadopoulos, On Thurston's boundary of Teichmüller space and the extension of earthquakes, 1988 Preprint. MR 967017
- [Rees] M. Rees An alternative approach to the ergodic theory of measured foliations on surfaces, Ergodic Theory and Dynamical Systems 1 (1981), 461-488. MR 662738
- [Bass-Serre] J.-P. Serre (with H. Bass), Trees, Dynamical Systems, Springer-Verlag, New York, 1980. MR 607504
- [Smale] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. MR 228014
- [Strebel] K. Strebel, Quadratic differentials, Springer-Verlag, Berlin, Heidelberg, New York and Tokyo, 1984. MR 743423
- [Sullivan] D. P. Sullivan, Travaux de Thurston sur les groupes quasi-fuchsiens et les variétés hyperboliques de dimension3 fîbrées sur S, Bourbaki Seminar (1979-80), 196-214, Lecture Notes in Math., vol. 842, Springer-Verlag, Berlin and New York, 1981. MR 636524
- [Th0] W. P. Thurston, The geometry and topology of three-manifolds, Princeton Math. Dept., 1979.
- [Th1] W. P. Thurston, Minimal stretch maps between hyperbolic surfaces, Topology (to appear).
- [Veech1] W. Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math. (2) 115 (1982), 201-242. MR 644019
- [Veech2] W. Veech, The Teichmüller geodesic flow, Ann. of Math. (2) 124 (1986), 441-530. MR 866707
- [Wald] F. Waldhausen, On irreducible manifolds which are sufficiently large, Ann. of Math. (2) 87 (1968), 56-88. MR 224099
- [Wolp1] S. Wolpert, On the symplectic geometry of deformations of a hyperbolic surface.
- [Zieschang] H. Zieschang, Finite groups of mapping classes of surfaces, Springer-Verlag, Berlin and New York, 1980. MR 643627
- 1.
- J. Nielsen, Surface transformation classes of algebraically finite type, Danske Vid. Selsk. Math.-Phys. Medd. 68 (1944). MR 15791
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Additional Information:
DOI:
10.1090/S0273-0979-1988-15685-6
PII:
S 0273-0979(1988)15685-6
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