Questions about Polynomial Matings
Xavier Buff[1]; Adam L. Epstein[2]; Sarah Koch[3]; Daniel Meyer[4]; Kevin Pilgrim[4]; Mary Rees[5]; Tan Lei[6]
- [1] Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France
- [2] Mathematics institute, University of Warwick, Coventry CV4 7AL, United Kingdom
- [3] Department of Mathematics, Science Center, 1 Oxford Street, Harvard University, Cambridge MA 02138, United States
- [4] Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
- [5] Department of Mathematical Sciences, University of Liverpool, Mathematics Building Peach St., Liverpool L69 7ZL U.K.
- [6] LUNAM Université, Université d’Angers, LAREMA – Laboratoire Angevin de Recherche en Mathématiques, 2 bd Lavoisier, 49045 Angers, cedex, France
Annales de la faculté des sciences de Toulouse Mathématiques (2012)
- Volume: 21, Issue: S5, page 1149-1176
- ISSN: 0240-2963
Access Full Article
topAbstract
topHow to cite
topBuff, Xavier, et al. "Questions about Polynomial Matings." Annales de la faculté des sciences de Toulouse Mathématiques 21.S5 (2012): 1149-1176. <http://eudml.org/doc/251009>.
@article{Buff2012,
abstract = {We survey known results about polynomial mating, and pose some open problems.},
affiliation = {Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France; Mathematics institute, University of Warwick, Coventry CV4 7AL, United Kingdom; Department of Mathematics, Science Center, 1 Oxford Street, Harvard University, Cambridge MA 02138, United States; Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany; Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany; Department of Mathematical Sciences, University of Liverpool, Mathematics Building Peach St., Liverpool L69 7ZL U.K.; LUNAM Université, Université d’Angers, LAREMA – Laboratoire Angevin de Recherche en Mathématiques, 2 bd Lavoisier, 49045 Angers, cedex, France},
author = {Buff, Xavier, Epstein, Adam L., Koch, Sarah, Meyer, Daniel, Pilgrim, Kevin, Rees, Mary, Lei, Tan},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
month = {12},
number = {S5},
pages = {1149-1176},
publisher = {Université Paul Sabatier, Toulouse},
title = {Questions about Polynomial Matings},
url = {http://eudml.org/doc/251009},
volume = {21},
year = {2012},
}
TY - JOUR
AU - Buff, Xavier
AU - Epstein, Adam L.
AU - Koch, Sarah
AU - Meyer, Daniel
AU - Pilgrim, Kevin
AU - Rees, Mary
AU - Lei, Tan
TI - Questions about Polynomial Matings
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2012/12//
PB - Université Paul Sabatier, Toulouse
VL - 21
IS - S5
SP - 1149
EP - 1176
AB - We survey known results about polynomial mating, and pose some open problems.
LA - eng
UR - http://eudml.org/doc/251009
ER -
References
top- Aspenberg (M.) & Yampolsky (M.).— Mating non-renormalizable quadratic polynomials, Commun. Math. Phys. 287, p. 1-40 (2009). Zbl1187.37065MR2480740
- Brock (J.), Canary (R.), and Minsky (Y.).— The classification of Kleinian surface groups II: the ending lamination conjecture, To appear, Annals of Mathematics. Zbl1253.57009MR2925381
- Buff (X.), Epstein (A.L.) & Koch (S.).— Twisted matings and equipotential gluing, in this volume. Zbl06167099
- Blé (G.) & Valdez (R.).— Mating a Siegel disk with the Julia set of a real quadratic polynomial, Conform. Geom. Dyn. 10, p. 257-284 (electronic) (2006). Zbl1185.37104MR2261051
- Bers (L.).— Simultaneous uniformization, Bull. Amer. Math. Soc. 66, p. 94-97 (1960). Zbl0090.05101MR111834
- Bullett (S.).— Matings in holomorphic dynamics, in Geometry of Riemann surfaces, London Math. Soc. Lecture Note Ser. 368, p. 88-119. Cambridge Univ. Press, Cambridge (2010). Zbl1206.30002MR2665006
- Cannon (J.) and Thurston (W.).— Group invariant Peano curves, Geometry and Topology 11, p. 1315-1355 (2007). Zbl1136.57009MR2326947
- Chéritat (A.).— Tan Lei and Shishikura’s example of non-mateable degree polynomials without a Levy cycle, in this volume. Zbl1320.37023
- Douady (A.) & Hubbard (J.H.).— A Proof of Thurston’s characterization of rational functions, Acta. Math. 171, p. 263-297 (1993). Zbl0806.30027MR1251582
- Dudko (D.).— Matings with laminations, arXiv:1112.4780
- Epstein (A.).— Quadratic mating discontinuity, manuscript (2012).
- Exall (F.).— Rational maps represented by both rabbit and aeroplane matings, PhD thesis, University of Liverpool (2011).
- Hruska Boyd (S.).— The Medusa algorithm for polynomial matings, arXiv:1102.5047. Zbl1291.37054
- Hubbard (J.).— Matings and the other side of the dictionary, in this volume. Zbl1283.37052
- Hubbard (J.).— Preface, in The Mandelbrot set, Theme and Variations, London Math. Soc. Lecture Note Series 274, p. xiii-xx. Cambridge University Press (2000). Zbl1107.37304MR1765081
- Haïssinsky (P.) & Tan (L.).— Convergence of pinching deformations and matings of geometrically finite polynomials, Fund. Math. 181, p. 143-188. Zbl1048.37045MR2070668
- Kameyama (A.).— On Julia sets of postcritically finite branched coverings. II. S1-parametrization of Julia sets. J. Math. Soc. Japan 55, p. 455-468 (2003). Zbl1162.37319MR1961296
- Kiwi (J.) & Rees (M.).— Counting hyperbolic components, submitted to the London Mathematical Society.
- Luo (J.).— Combinatorics and holomorphic dynamics: Captures, matings, Newton’s method, Ph.D. Thesis, Cornell University (1995). MR2691795
- Minsky (Y.).— On Thurston’s ending lamination conjecture, in Low-dimensional topology (Knoxville, TN, 1994), Conf. Proc. Lecture Notes Geom. Topology, III, p. 109-122. Int. Press, Cambridge, MA (1994). Zbl0846.57010MR1316176
- Mashanova (I.) & Timorin (V.).— Captures, matings, and regulings, arxiv:1111.5696.
- Meyer (D.).— Expanding Thurston maps as quotients, http://arxiv.org/abs/0910.2003.
- Meyer (D.).— Invariant Peano curves of expanding Thurston maps, to appear, Acta. Math., http://arxiv.org/abs/0907.1536. Zbl1333.37043
- Meyer (D.).— Unmating of rational maps, sufficient criteria and examples, arXiv:1110.6784, (2011), to appear in the Proc. to Milnor’s 80th birthday. Zbl06490013
- Meyer (D.) & Petersen (C.).— On the notions of matings, in this volume.
- Milnor (J.).— Pasting together Julia sets; a worked out example of mating, Experimental Math 13 p. 55-92 (2004). Zbl1115.37051MR2065568
- Milnor (J.) and Tan (L.).— Remarks on quadratic rational maps (with an appendix by Tan Lei), Experimental Math 2, p. 37-83 (1993). Zbl0922.58062MR1246482
- Mj (M.).— Cannon-Thurston maps for surface groups II: split geometry and the Minsky model, http://lists.rkmvu.ac.in/intro/academics/matsc_website/mahan/split.pdf, preprint; accessed June 11 (2012).
- Mj (M.).— Cannon-Thurston maps for surface groups, http://arxiv.org/pdf/math.GT/0607509.pdf, preprint. Zbl1301.57013
- Petersen (C.).— No elliptic limits for quadratic rational maps, Ergodic Theory Dynam. Systems 19, p. 127-141 (1999). Zbl0921.30019MR1676926
- Rees (M.).— Realization of matings of polynomials of rational maps of degree two, Manuscript (1986).
- Rees (M.).— Components of degree two hyperbolic rational maps, Invent. Math., 100, p. 357-382 (1990). Zbl0712.30022MR1047139
- Rees (M.).— A partial description of parameter space of rational maps of degree two: part I, Acta Math., 168 p. 11-87 (1992). Zbl0774.58035MR1149864
- Rees (M.).— Multiple equivalent matings with the aeroplane polynomial, Erg. Th. and Dyn. Sys., 30, p. 1239-1257 (2010). Zbl1291.37069MR2669420
- Sharland (T.).— Rational Maps with Clustering and the Mating of Polynomials, PhD thesis, Warwick (2010).
- Sharland (T.).— Constructing rational maps with cluster points using the mating operation, Preprint (2011). Zbl1333.37033
- Shishikura (M.).— On a theorem of M. Rees for matings of polynomials, London Math. Soc. Lecture Note Ser., 274. CMP 2000:14. Zbl1062.37039MR1765095
- Shishikura (M.) & Tan (L.).— A family of cubic rational maps and matings of cubic polynomials, Experiment. Math. 9, p. 29-53 (2000). Zbl0969.37020MR1758798
- Tan (L.).— Branched coverings and cubic Newton maps, Fund. Math. 154, p. 207-260 (1997). Zbl0903.58029MR1475866
- Tan (L.).— Matings of quadratic polynomials, Erg. Th. and Dyn. Sys. 12, p. 589-620 (1992). Zbl0756.58024MR1182664
- Tan (L.).— On pinching deformations of rational maps, Ann. Sci. École Norm. Sup. 35, p. 353-370 (2002). Zbl1041.37022MR1914001
- Wittner (B.).— On the bifurcation loci of rational maps of degree two, Ph.D. thesis, Cornell University (1988). MR2636558
- Yampolsky (M.) & Zakeri (S.).— Mating Siegel quadratic polynomials, Journ. of the A.M.S., vol 14-1, p. 25-78 (2000). Zbl1050.37022MR1800348
- Zhang (G.).— All David type Siegel disks of polynomial maps are Jordan domains, manuscript (2009).
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.