On The Notions of Mating

Carsten Lunde Petersen[1]; Daniel Meyer[2]

  • [1] Institut for Natur, Systemer og Modeller Bygn 27.2, Roskilde Universitet, Universitetsvej 1, DK-4000 Roskilde, Denmark
  • [2] Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany

Annales de la faculté des sciences de Toulouse Mathématiques (2012)

  • Volume: 21, Issue: S5, page 839-876
  • ISSN: 0240-2963

Abstract

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The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations between the polynomials and their matings are discussed and proved. Finally holomorphic motion properties of slow-mating are proved.

How to cite

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Petersen, Carsten Lunde, and Meyer, Daniel. "On The Notions of Mating." Annales de la faculté des sciences de Toulouse Mathématiques 21.S5 (2012): 839-876. <http://eudml.org/doc/250988>.

@article{Petersen2012,
abstract = {The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations between the polynomials and their matings are discussed and proved. Finally holomorphic motion properties of slow-mating are proved.},
affiliation = {Institut for Natur, Systemer og Modeller Bygn 27.2, Roskilde Universitet, Universitetsvej 1, DK-4000 Roskilde, Denmark; Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany},
author = {Petersen, Carsten Lunde, Meyer, Daniel},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
month = {12},
number = {S5},
pages = {839-876},
publisher = {Université Paul Sabatier, Toulouse},
title = {On The Notions of Mating},
url = {http://eudml.org/doc/250988},
volume = {21},
year = {2012},
}

TY - JOUR
AU - Petersen, Carsten Lunde
AU - Meyer, Daniel
TI - On The Notions of Mating
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2012/12//
PB - Université Paul Sabatier, Toulouse
VL - 21
IS - S5
SP - 839
EP - 876
AB - The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations between the polynomials and their matings are discussed and proved. Finally holomorphic motion properties of slow-mating are proved.
LA - eng
UR - http://eudml.org/doc/250988
ER -

References

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  2. Branner (B.) and Hubbard (J. H.).— The iteration of cubic polynomials : Part I. The global topology of parameter space. Acta Math. 160, p. 143-206 (1988). Zbl0668.30008MR945011
  3. Carleson (L.) and Gamelin (T.).— Introduction to complex Dynamics. Springer (1993). Zbl0782.30022MR1230383
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  8. Meyer (D.).— Expanding Thurston maps as quotients. Preprint. 
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  10. Milnor (J.).— Dynamics in one complex variable, Princeton Univ. Press, Princeton, NJ, (2006). Zbl1085.30002MR2193309
  11. Milnor (J.).— Geometry and Dynamics of Quadratic Rational Maps. Exp. Math. 2, p. 37-83 (1993). Zbl0922.58062MR1246482
  12. Milnor (J.).— Pasting together Julia sets: A worked out example of mating. Exp. Math. 13(1), p. 55-92 (2004). Zbl1115.37051MR2065568
  13. Moore (R. L.).— Concerning upper semi-continuous collections of continua, Trans. Amer. Math. Soc. Vol 27 No. 4, p. 416-428 (1925). Zbl51.0464.03MR1501320
  14. Petersen (C. L.) and Tan (L.).— Branner-Hubbard motions and attracting dynamics. in Dynamics on the Riemann Sphere, edited by P. G. Hjorth and C. L. Petersen, EMS Publishing House, p. 45-70 (2006). Zbl1149.37312MR2348954
  15. Rees (M.).— A partial description of parameter space of rational maps of degree two. I.Acta Math., 168(1-2), p. 11-87 (1992). Zbl0774.58035MR1149864
  16. Tan (L.).— Matings of quadratic polynomials.Ergodic Theory Dynam. Systems, 12(3), p. 589-620, (1992). Zbl0756.58024MR1182664
  17. Timorin (V.).— Moore’s theorem, preprint. 
  18. Shishikuran (M.).— On a Theorem of M. Rees for matings of polynomials in The Mandelbrot Set, Theme and Variations, edited by Tan lei, Cambridge University Press, p. 289-305 (2000). Zbl1062.37039MR1765095
  19. Yampolsky (M.) and Zakeri (S.).— Mating Siegel quadratic polynomials, J. Amer. Math. Soc., 14(1), p. 25-78 (2001). Zbl1050.37022MR1800348

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