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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). |
[2] |
Martin R. Bridson and André Haefliger, "Metric spaces of non-positive curvature,", Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 319 (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.
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.
doi: 10.1007/s10711-009-9352-7. |
[6] |
Robert J. Daverman, "Decompositions of Manifolds,", Pure and Applied Mathematics, 124 (1986).
|
[7] |
Adrien Douady and John Hubbard, A proof of Thurston's topological characterization of rational functions,, Acta. Math., 171 (1993), 263.
doi: 10.1007/BF02392534. |
[8] |
Peter Haïssinsky and Kevin M. Pilgrim, Coarse expanding conformal dynamics,, Astérisque, 325 (2009).
|
[9] |
Peter Haïssinsky and Kevin M. Pilgrim, Finite type coarse expanding conformal dynamics,, Groups Geom. Dyn., 5 (2011), 603.
doi: 10.4171/GGD/141. |
[10] |
Volodymyr Nekrashevych, "Self-Similar Groups,", Mathematical Surveys and Monographs, 117 (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, (2000), 349.
|
[13] |
Kevin M. Pilgrim, Julia sets as Gromov boundaries following V. Nekrashevych,, Spring Topology and Dynamical Systems Conference, 29 (2005), 293.
|
[14] |
Mary Rees, A partial description of parameter space of rational maps of degree two. I,, Acta Math., 168 (1992), 11.
doi: 10.1007/BF02392976. |
[15] |
Michael Shub, Endomorphisms of compact differentiable manifolds,, Amer. J. Math., 91 (1969), 175.
|
show all references
References:
[1] |
Laurent Bartholdi, Functionally recursive groups,, GAP package, (2011). |
[2] |
Martin R. Bridson and André Haefliger, "Metric spaces of non-positive curvature,", Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 319 (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.
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.
doi: 10.1007/s10711-009-9352-7. |
[6] |
Robert J. Daverman, "Decompositions of Manifolds,", Pure and Applied Mathematics, 124 (1986).
|
[7] |
Adrien Douady and John Hubbard, A proof of Thurston's topological characterization of rational functions,, Acta. Math., 171 (1993), 263.
doi: 10.1007/BF02392534. |
[8] |
Peter Haïssinsky and Kevin M. Pilgrim, Coarse expanding conformal dynamics,, Astérisque, 325 (2009).
|
[9] |
Peter Haïssinsky and Kevin M. Pilgrim, Finite type coarse expanding conformal dynamics,, Groups Geom. Dyn., 5 (2011), 603.
doi: 10.4171/GGD/141. |
[10] |
Volodymyr Nekrashevych, "Self-Similar Groups,", Mathematical Surveys and Monographs, 117 (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, (2000), 349.
|
[13] |
Kevin M. Pilgrim, Julia sets as Gromov boundaries following V. Nekrashevych,, Spring Topology and Dynamical Systems Conference, 29 (2005), 293.
|
[14] |
Mary Rees, A partial description of parameter space of rational maps of degree two. I,, Acta Math., 168 (1992), 11.
doi: 10.1007/BF02392976. |
[15] |
Michael Shub, Endomorphisms of compact differentiable manifolds,, Amer. J. Math., 91 (1969), 175.
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