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An algebraic characterization of expanding Thurston maps
1. | Université Paul Sabatier, Institut de Mathématiques de Toulouse (IMT), 118 route de Narbonne, 31062 Toulouse Cedex 9, France |
2. | Dept. Mathematics, Indiana University, Bloomington, IN 47405 |
References:
[1] |
Laurent Bartholdi, Functionally recursive groups, GAP package, 2011. Available from: http://www.uni-math.gwdg.de/laurent/FR/. |
[2] |
Martin R. Bridson and André Haefliger, "Metric spaces of non-positive curvature," Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 319, Springer-Verlag, Berlin, 1999. |
[3] |
Mario Bonk and Daniel Meyer, Expanding Thurston maps, arXiv:1009.3647, 2010. |
[4] |
James W. Cannon, William J. Floyd and Walter R. Parry, Finite subdivision rules, Conform. Geom. Dyn., 5 (2001), 153-196 (electronic).
doi: 10.1090/S1088-4173-01-00055-8. |
[5] |
James W. Cannon, William J. Floyd, Walter R. Parry and Kevin Pilgrim, Subdivision rules and virtual endomorphisms, Geom. Dedicata, 141 (2009), 181-195.
doi: 10.1007/s10711-009-9352-7. |
[6] |
Robert J. Daverman, "Decompositions of Manifolds," Pure and Applied Mathematics, 124, Academic Press, Inc., Orlando, FL, 1986. |
[7] |
Adrien Douady and John Hubbard, A proof of Thurston's topological characterization of rational functions, Acta. Math., 171 (1993), 263-297.
doi: 10.1007/BF02392534. |
[8] |
Peter Haïssinsky and Kevin M. Pilgrim, Coarse expanding conformal dynamics, Astérisque, 325 (2009), viii+139 pp. (2010). |
[9] |
Peter Haïssinsky and Kevin M. Pilgrim, Finite type coarse expanding conformal dynamics, Groups Geom. Dyn., 5 (2011), 603-661.
doi: 10.4171/GGD/141. |
[10] |
Volodymyr Nekrashevych, "Self-Similar Groups," Mathematical Surveys and Monographs, 117, American Mathematical Society, Providence, RI, 2005. |
[11] |
Volodymyr Nekrashevych, Combinatorial models of expanding dynamical systems,, \arXiv{0810.4936}., ().
|
[12] |
Kevin Pilgrim and Tan Lei, Rational maps with disconnected Julia set, Géométrie Complexe et Systèmes Dynamiques (Orsay, 1995), Astérisque, (2000), xiv, 349-384. |
[13] |
Kevin M. Pilgrim, Julia sets as Gromov boundaries following V. Nekrashevych, Spring Topology and Dynamical Systems Conference, Topology Proc., 29 (2005), 293-316. |
[14] |
Mary Rees, A partial description of parameter space of rational maps of degree two. I, Acta Math., 168 (1992), 11-87.
doi: 10.1007/BF02392976. |
[15] |
Michael Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math., 91 (1969), 175-199. |
show all references
References:
[1] |
Laurent Bartholdi, Functionally recursive groups, GAP package, 2011. Available from: http://www.uni-math.gwdg.de/laurent/FR/. |
[2] |
Martin R. Bridson and André Haefliger, "Metric spaces of non-positive curvature," Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 319, Springer-Verlag, Berlin, 1999. |
[3] |
Mario Bonk and Daniel Meyer, Expanding Thurston maps, arXiv:1009.3647, 2010. |
[4] |
James W. Cannon, William J. Floyd and Walter R. Parry, Finite subdivision rules, Conform. Geom. Dyn., 5 (2001), 153-196 (electronic).
doi: 10.1090/S1088-4173-01-00055-8. |
[5] |
James W. Cannon, William J. Floyd, Walter R. Parry and Kevin Pilgrim, Subdivision rules and virtual endomorphisms, Geom. Dedicata, 141 (2009), 181-195.
doi: 10.1007/s10711-009-9352-7. |
[6] |
Robert J. Daverman, "Decompositions of Manifolds," Pure and Applied Mathematics, 124, Academic Press, Inc., Orlando, FL, 1986. |
[7] |
Adrien Douady and John Hubbard, A proof of Thurston's topological characterization of rational functions, Acta. Math., 171 (1993), 263-297.
doi: 10.1007/BF02392534. |
[8] |
Peter Haïssinsky and Kevin M. Pilgrim, Coarse expanding conformal dynamics, Astérisque, 325 (2009), viii+139 pp. (2010). |
[9] |
Peter Haïssinsky and Kevin M. Pilgrim, Finite type coarse expanding conformal dynamics, Groups Geom. Dyn., 5 (2011), 603-661.
doi: 10.4171/GGD/141. |
[10] |
Volodymyr Nekrashevych, "Self-Similar Groups," Mathematical Surveys and Monographs, 117, American Mathematical Society, Providence, RI, 2005. |
[11] |
Volodymyr Nekrashevych, Combinatorial models of expanding dynamical systems,, \arXiv{0810.4936}., ().
|
[12] |
Kevin Pilgrim and Tan Lei, Rational maps with disconnected Julia set, Géométrie Complexe et Systèmes Dynamiques (Orsay, 1995), Astérisque, (2000), xiv, 349-384. |
[13] |
Kevin M. Pilgrim, Julia sets as Gromov boundaries following V. Nekrashevych, Spring Topology and Dynamical Systems Conference, Topology Proc., 29 (2005), 293-316. |
[14] |
Mary Rees, A partial description of parameter space of rational maps of degree two. I, Acta Math., 168 (1992), 11-87.
doi: 10.1007/BF02392976. |
[15] |
Michael Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math., 91 (1969), 175-199. |
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