Captures, matings and regluings

Inna Mashanova[1]; Vladlen Timorin[2]

  • [1] Faculty of Mathematics and Laboratory of Algebraic Geometry, National Research University Higher School of Economics, 7 Vavilova St 117312 Moscow, Russia Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, MI 48109-1043 USA
  • [2] Independent University of Moscow, Bolshoy Vlasyevskiy Pereulok 11, 119002 Moscow, Russia

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

  • Volume: 21, Issue: S5, page 877-906
  • ISSN: 0240-2963

Abstract

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In parameter slices of quadratic rational functions, we identify arcs represented by matings of quadratic polynomials. These arcs are on the boundaries of hyperbolic components.

How to cite

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Mashanova, Inna, and Timorin, Vladlen. "Captures, matings and regluings." Annales de la faculté des sciences de Toulouse Mathématiques 21.S5 (2012): 877-906. <http://eudml.org/doc/251023>.

@article{Mashanova2012,
abstract = {In parameter slices of quadratic rational functions, we identify arcs represented by matings of quadratic polynomials. These arcs are on the boundaries of hyperbolic components.},
affiliation = {Faculty of Mathematics and Laboratory of Algebraic Geometry, National Research University Higher School of Economics, 7 Vavilova St 117312 Moscow, Russia Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, MI 48109-1043 USA; Independent University of Moscow, Bolshoy Vlasyevskiy Pereulok 11, 119002 Moscow, Russia},
author = {Mashanova, Inna, Timorin, Vladlen},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
month = {12},
number = {S5},
pages = {877-906},
publisher = {Université Paul Sabatier, Toulouse},
title = {Captures, matings and regluings},
url = {http://eudml.org/doc/251023},
volume = {21},
year = {2012},
}

TY - JOUR
AU - Mashanova, Inna
AU - Timorin, Vladlen
TI - Captures, matings and regluings
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2012/12//
PB - Université Paul Sabatier, Toulouse
VL - 21
IS - S5
SP - 877
EP - 906
AB - In parameter slices of quadratic rational functions, we identify arcs represented by matings of quadratic polynomials. These arcs are on the boundaries of hyperbolic components.
LA - eng
UR - http://eudml.org/doc/251023
ER -

References

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  1. Aspenberg (M.), Yampolsky (M.).— “Mating non-renormalizable quadratic polynomials”, Commun. Math. Phys., 287, p. 1-40 (2009). Zbl1187.37065MR2480740
  2. Douady (A.) and Hubbard (J.).— “A proof of Thurston’s topological characterization of rational functions”, Acta Math. 171, p. 263-297 (1993). Zbl0806.30027MR1251582
  3. McMullen (C.).— “Automorphisms of rational maps”, In “Holomorphic Functions and Moduli I”, p. 31-60, Springer, (1988). Zbl0692.30035MR955807
  4. Moore (R.L.).— “On the foundations of plane analysis situs”, Transactions of the AMS, 17, p. 131-164 (1916). MR1501033
  5. Moore (R.L.).— “Concerning upper-semicontinuous collections of continua”, Transactions of the AMS, 27, Vol. 4, p. 416-428 (1925). Zbl51.0464.03MR1501320
  6. Mañe (R.), Sud (P.), Sullivan (D.).— “On the dynamics of rational maps”, Ann. Sci. École Norm. Sup. (4) 16, no. 2, p. 193-217 (1983). Zbl0524.58025MR732343
  7. Milnor (J.).— “Geometry and Dynamics of Quadratic Rational Maps” Experimental Math. 2 p. 37-83 (1993). Zbl0922.58062MR1246482
  8. Milnor (J.).— “Periodic orbits, externals rays and the Mandelbrot set: an expository account”. Géométrie complexe et systèmes dynamiques (Orsay, 1995). Astérisque No. 261, p. 277-333 (2000). Zbl0941.30016MR1755445
  9. Milnor (J.).— “Local connectivity of Julia sets: expository lectures”, in “The Mandelbrot set, Theme and Variations,” LMS Lecture Note Series 274, Cambr. U. Press, p. 67-116 (2000). Zbl1107.37305MR1765085
  10. Pilgrim (K.).— “Rational maps whose Fatou components are Jordan domains”, Ergodic Theory and Dynamical Systems, 16, p. 1323-1343 (1996). Zbl0894.30017MR1424402
  11. Rees (M.).— “Components of degree two hyperbolic rational maps” Invent. Math. 100, p. 357-382 (1990). Zbl0712.30022MR1047139
  12. Rees (M.).— “A partial description of the Parameter Space of Rational Maps of Degree Two: Part 1” Acta Math. 168, 11-87 (1992). Zbl0774.58035MR1149864
  13. Rees (M.).— “A Fundamental Domain for V 3 ”, Mém. Soc. Math. Fr. (N.S.) No. 121 (2010). Zbl1222.30001MR2768577
  14. Sullivan (D.).— “ Quasiconformal homeomorphisms and dynamics. I. Solution of the Fatou-Julia problem on wandering domains”. Ann. of Math. (2) 122, No. 3, p. 401-418 (1985). Zbl0589.30022MR819553
  15. Tan (L.).— “Matings of quadratic polynomials”, Erg. Th. and Dyn. Sys. 12 p. 589-620 (1992). Zbl0756.58024MR1182664
  16. Thurston (W.).— “Geometry and dynamics of rational functions”, in “Complex dynamics: families and friends”, D. Schleicher (Ed.) (2009) MR2508255
  17. Timorin (V.).— “Topological regluing of rational functions”, Inventiones Math., 179, Issue 3, p. 461-506 (2009). Zbl1211.37058MR2587338
  18. Wittner (B.).— “On the bifurcation loci of rational maps of degree two”, PhD Thesis, Cornell University (1988). MR2636558

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