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Journal of Topology Advance Access published online on March 3, 2009
Journal of Topology, doi:10.1112/jtopol/jtn032
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© 2009 London Mathematical Society

Ribbon R-trees and holomorphic dynamics on the unit disk

Curtis T. McMullen

Mathematics Department, Harvard University, 1 Oxford Street, Cambridge, MA 02138-2901, USA

Received December 1, 2007.

2000 Mathematics Subject Classification 37F, 20E08

This research was supported in part by the National Science Foundation.



References

  1. Ahlfors L. Conformal invariants: topics in geometric function theory (1973) McGraw-Hill.
  2. Bestvina M. Degenerations of the hyperbolic space. Duke Math. J. (1988) 56:143–161.[CrossRef]
  3. Bestvina M. R-trees in topology, geometry and group theory. In: Handbook of geometry and topology (2002) Elsevier. 55–91.
  4. Bonahon F. Bouts des variétés hyperboliques de dimension 3. Ann. Math. (1986) 124:71–158.[CrossRef]
  5. Bonahon F. The geometry of Teichmüller space via geodesic currents. Invent. Math. (1988) 92:139–162.[CrossRef]
  6. Branner B., Fagella N. Homeomorphisms between limbs of the Mandelbrot set. J. Geom. Anal. (1999) 9:327–390.
  7. Chiswell I. M. Nonstandard analysis and the Morgan–Shalen compactification. Quart. J. Math. Oxford Ser. (2) (1991) 42:257–270.[CrossRef]
  8. Cornfeld I. P., Fomin S. V., Sinai Ya. G. Ergodic theory (1982) Springer.
  9. DeMarco L. Iteration at the boundary of the space of rational maps. Duke Math. J. (2005) 130:169–197.[CrossRef]
  10. DeMarco L. The moduli space of quadratic rational maps. J. Am. Math. Soc. (2007) 20:321–355.[CrossRef]
  11. DeMarco L., McMullen C. Trees and the dynamics of polynomials. Ann. scient. Éc. Norm. Sup. (2008) 41:337–383.
  12. Douady A., Hubbard J. Étude dynamique des polynômes complexes. Pub. Math. d'Orsay. 84–2. 85–4 (1985).
  13. Emerson N. D. Dynamics of polynomials with disconnected Julia sets. Discrete Contin. Dyn. Syst. (2003) 9:801–834.[CrossRef]
  14. Epstein A. L. Bounded hyperbolic components of quadratic rational maps. Ergodic Theory Dynam. Systems (2000) 20:727–748.[CrossRef]
  15. Fock V., Goncharov A. Moduli spaces of local systems and higher Teichmüller theory. Publ. Math. IHES (2006) 103:1–211.[CrossRef]
  16. Ghys E., de la Harpe P., eds. Sur les groups hyperboliques d'après Mikhael Gromov (1990) Birkhäuser.
  17. Goldberg L. Fixed points of polynomial maps I. Rotation subsets of the circles. Ann. Sci. École Norm. Sup. (1992) 25:679–685.
  18. Goldberg L. R., Milnor J. Fixed points of polynomial maps II: fixed point portraits. Ann. Sci. École Norm. Sup. (1993) 26:51–98.
  19. Gromov M. Metric structures for Riemannian and non-Riemannian spaces (2001) Birkhäuser.
  20. Keller K. Invariant factors, Julia equivalences and the (Abstract) Mandelbrot set (2000) Springer. Lecture Notes in Mathematics 1732.
  21. Kiwi J. Real laminations and the topological dynamics of complex polynomials. Adv. Math. (2004) 184:207–267.[CrossRef]
  22. Kiwi J. Puiseux series of polynomial dynamics and iteration of complex cubic polynomials. Ann. Inst. Fourier (2006) 56:1337–1404.
  23. Kontsevich M. Intersection theory on the moduli space of curves and the matrix Airy function. Comm. Math. Phys. (1992) 147:1–23.[CrossRef]
  24. McMullen C. Complex dynamics and renormalization (1994) 135. Princeton, NJ: Princeton University Press. Annals of Mathematics Studies.
  25. McMullen C. Thermodynamics, dimension and the Weil–Petersson metric. Invent. Math. (2008) 173:365–425.[CrossRef]
  26. McMullen C. A compactification of the space of expanding maps on the circle. Geom. Funct. Anal. to appear.
  27. McMullen C. Dynamics on the unit disk: short geodesics and simple cycles. Preprint, 7/2007.
  28. Milnor J. Geometry and dynamics of quadratic rational maps. Experiment. Math. (1993) 2:37–83.
  29. Milnor J. Periodic points, external rays and the Mandelbrot set: an expository account (2000) 277–333. Géométrie complexe et systèmes dynamiques, Astérisque 261.
  30. Minsky Y. On rigidity, limit sets, and end invariants of hyperbolic 3-manifolds. J. Am. Math. Soc. (1994) 7:539–588.[CrossRef]
  31. Morgan J., Shalen P. Valuations, trees, and degenerations of hyperbolic structures, I. Ann. of Math. (1984) 120:401–476.[CrossRef]
  32. Morgan J., Shalen P. An introduction to compactifying spaces of hyperbolic structures by actions on trees. In: Geometry and topology (1985) Springer. 228–240. Lecture Notes in Mathematics 1167.
  33. Otal J.-P. Le spectre marqué des longeurs des surfaces à courbure négative. Ann. Math. (1990) 131:151–162.[CrossRef]
  34. Otal J.-P. Le théorème d'hyperbolisation pour les variétés fibrées de dimension trois. Astérisque (1996) 235.
  35. Paulin F. Topologie de Gromov équivariante, structures hyperboliques et arbres réels. Invent. math. (1988) 94:53–80.[CrossRef]
  36. Paulin F. Actions de groupes sur les arbres. Séminaire Bourbaki, 1995/96, 98–137. Astérisque (1997) 241.
  37. Penner R. Perturbative series and the moduli space of Riemann surfaces. J. Differential Geom. (1988) 27:35–53.
  38. Petersen C. L. Local connectivity of some Julia sets containing a circle with an irrational rotation. Acta Math. (1996) 177:163–224.[CrossRef]
  39. Poirier A. On post critically finite polynomials, Part two: Hubbard trees. Preprint Stony Brook IMS 1993/5.
  40. Shishikura M. Trees associated with the configuration of Herman rings. Ergod. Th. & Dynam. Sys. (1989) 9:543–560.
  41. Shub M. Endomorphisms of compact differentiable manifolds. Am. J. Math. (1969) 91:175–199.[CrossRef]
  42. Shub M., Sullivan D. Expanding endomorphisms of the circle revisited. Ergodic Theory Dynam. Systems (1985) 5:285–289.
  43. Silverman J. The space of rational maps on P1. Duke Math. J. (1998) 94:41–77.[CrossRef]
  44. Sturmfels B. Solving systems of polynomial equations. (2002) Providence, RI: American Mathematical Society. CBMS Regional Conference Series in Mathematics 97.
  45. Thom R. L'equivalence d'une fonction différentiable et d'un polynôme. Topology (1965) 3:297–307.[CrossRef]
  46. Thurston W. P. Geometry and topology of three-manifolds (1979) Princeton, NJ: Princeton University Press. Lecture Notes.
  47. Wolff M. Sur les composantes exotiques des espaces d'actions de groupes de surfaces sur le plan hyperbolique. Thesis, Université de Grenoble I, 2007.

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This Article
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