On pinching deformations of rational maps

Lei Tan

Annales scientifiques de l'École Normale Supérieure (2002)

  • Volume: 35, Issue: 3, page 353-370
  • ISSN: 0012-9593

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Tan, Lei. "On pinching deformations of rational maps." Annales scientifiques de l'École Normale Supérieure 35.3 (2002): 353-370. <http://eudml.org/doc/82573>.

@article{Tan2002,
author = {Tan, Lei},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {rational map; Julia set; topological deformation},
language = {eng},
number = {3},
pages = {353-370},
publisher = {Elsevier},
title = {On pinching deformations of rational maps},
url = {http://eudml.org/doc/82573},
volume = {35},
year = {2002},
}

TY - JOUR
AU - Tan, Lei
TI - On pinching deformations of rational maps
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2002
PB - Elsevier
VL - 35
IS - 3
SP - 353
EP - 370
LA - eng
KW - rational map; Julia set; topological deformation
UR - http://eudml.org/doc/82573
ER -

References

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  1. [1] Beardon A., Iteration of Rational Functions, Springer-Verlag, 1991. Zbl0742.30002MR1128089
  2. [2] Cui G., Geometrically finite rational maps with given combinatorics, preprint, February 1997. 
  3. [3] Cui G., Deformations of geometrically finite rational maps, April 1997. 
  4. [4] Haïssinsky P., Pincement de polynômes, to appear. Zbl1146.37347MR1898391
  5. [5] Makienko P., Unbounded components in parameter space of rational maps, in: Conformal Geometry and Dynamics, Vol. 4, 2000, pp. 1-21. Zbl0948.37032MR1741344
  6. [6] McMullen C., Complex Dynamics and Renormalization, Ann. Math. Studies, 135, Princeton Univ. Press, 1994. Zbl0822.30002MR1312365
  7. [7] McMullen C., Sullivan D., Quasiconformal homeomorphisms and dynamics III: The Teichmüller space of a holomorphic dynamical system, Adv. Math.135 (1998) 351-395. Zbl0926.30028MR1620850
  8. [8] Milnor J., Dynamics in One Complex Variable: Introductory Lectures, Vieweg, 1999. Zbl0946.30013MR1721240
  9. [9] Petersen C., No elliptic limits for quadratic maps, Ergodic Theory Dynamical Systems19 (1999) 127-141. Zbl0921.30019MR1676926
  10. [10] Petersen C., On the Pommerenke–Levin–Yoccoz inequality, Ergodic Theory Dynamical Systems13 (1993) 785-806. Zbl0802.30022MR1257034
  11. [11] Pilgrim K., Cylinders for iterated rational maps, Ph.D. Thesis, University of California, Berkeley, 1994. 
  12. [12] Pilgrim K., Tan L., Combining rational maps and controlling obstructions, Ergodic Theory Dynamical Systems18 (1998) 221-246. Zbl0915.58043MR1609463
  13. [13] Pilgrim K., Tan L., On disc-annulus surgery of rational maps, in: Jiang Y., Wen L. (Eds.), Proceedings of the International Conference in Dynamical Systems in Honor of Professor Liao Shan-tao 1998, World Scientific, 1999, pp. 237-250. 
  14. [14] Tan L., Branched coverings and cubic Newton maps, Fundamenta Mathematicae154 (1997) 207-260. Zbl0903.58029MR1475866
  15. [15] Tan L., Continuous and discrete Newton's algorithms, in: Proceedings of the Conference on Complex Analysis, Nankai Institute of Mathematics, 1992, International Press, 1994, pp. 208-219. Zbl0824.65029MR1343510

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