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Experimental Mathematics Volume 17, 2008 - Issue 3
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Original Article

The Minimal Dilatation of a Genus-Two Surface

Jin-Hwan Cho Department of Mathematics, The University of Suwon, San 2-2 Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, Korea
&
Ji-Young Ham Department of Mathematical Sciences, Seoul National University, San 56-1 Shinrim-dong Kwanak-gu, Seoul, 151-747, Korea
Pages 257-267 | Published online: 30 Jan 2011

  • A. Papadopoulos and R. C. Penner. "A Characterization of Pseudo-Anosov Foliations." Pacific J. Math. 130 (1987), 359–377.
  • R. C. Penner. "Bounds on Least Dilatations." Proc. Amer. Math. Soc. 113 (1991), 443–450.
  • E. Rykken. "Expanding Factors for Pseudo-Anosov Homeomorphisms." Michigan Math. J. 46 (1999), 281–296.
  • W. T. Song, K. H. Ko, and J. E. Los. "Entropies of Braids." J. Knot Theory Ramifications 11 (2002), 647–666.
  • A. Y. Zhirov. "On the Minimum of the Dilatation of Pseudo-Anosov Diffeomorphisms of a Pretzel." Russ. Math. Surv. 50 (1995), 223–224.
  • W. Abikoff. The Real Analytic Theory of Teichmüller Space, Lecture Notes in Math., 820. New York: Springer, 1980.
  • M. Bauer. "An Upper Bound for the Least Dilatation." Trans. Amer. Math. Soc. 330 (1992), 361–370.
  • M. Bestvina and M. Handel. "Train-Tracks for Surface Homeomorphisms." Topology 34 (1995), 109–140.
  • S. Bigelow and R. Budney. "The Mapping Class Group of a Genus Two Surface Is Linear." Algebraic & Geometric Topology 1 (2001), 699–708.
  • J. S. Birman. Braids, Links and Mapping Class Groups, Annals of Math Studies, 82. Princeton: Princeton Univ. Press, 1974.
  • J. S. Birman and H. M. Hilden. "Mapping Class Groups of Closed Surfaces as Covering Spaces." In Advances in the Theory of Riemann Surfaces, pp. 81–115, Annals of Math. 66. Princeton: Princeton Univ. Press, 1971.
  • J. S. Birman and H. M. Hilden. "On Isotopies of Homeomorphisms of Riemann Surfaces." Annals of Math. 97 (1973), 424–439.
  • P. Brinkmann. "An Implementation of the Bestvina–Handel Algorithm for Surface Homeomorphisms." Experiment. Math. 9:2 (2000), 235–240.
  • A. Casson and B. Steven. Automorphisms of Surfaces after Nielsen and Thurston, Londom Mathematical Society Student Texts, 9. Cambridge: Cambridge University Press, 1988.
  • A. Fathi, F. Laudenbach, and V. Poénaru. Travaux de Thurston sur les surfaces, Astérisque, 66–67. Paris: Société Mathématique de France, 1979.
  • J. Ham. "The Minimum Dilatation of 4 and 5 Braids." PhD thesis, University of California, Santa Barbara, 2006.
  • J. Ham and W. T. Song. "The Minimum Dilatation of Pseudo-Anosov 5-Braids." Experiment. Math. 16 (2007), 224–229.
  • M. Handel. "The Forcing Partial Order on the Three Times Punctured Disk." Ergodic Theory Dynam. Systems 17 (1997), 593–610.
  • E. Hironaka and E. Kin. "A Family of Pseudo-Anosov Braids with Small Dilatation." Algebr. Geom. Topol. 6 (2006), 699–738.
  • C. J. Leininger. "On Groups Generated by Two Positive Multi-twists: Teichmüller Curves and Lehmer's Number." Geom. Topol. 8 (2004), 1301–1359.
  • D. D. Long. "Constructing Pseudo-Anosov Maps." In Knots and Manifolds, pp. 108–114, Springer Lecture Notes 1144. New York: Springer, 1985.
  • T. Matsuoka. "Braids of Periodic Points and a 2-Dimensional Analogue of Sharkovskii's Ordering." Dynamical Systems and Nonlinear Oscillation phenomena 574 (1985), 241–255.

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