Perturbations of flexible Lattès maps

Xavier Buff; Thomas Gauthier

Bulletin de la Société Mathématique de France (2013)

  • Volume: 141, Issue: 4, page 603-614
  • ISSN: 0037-9484

Abstract

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We prove that any Lattès map can be approximated by strictly postcritically finite rational maps which are not Lattès maps.

How to cite

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Buff, Xavier, and Gauthier, Thomas. "Perturbations of flexible Lattès maps." Bulletin de la Société Mathématique de France 141.4 (2013): 603-614. <http://eudml.org/doc/272700>.

@article{Buff2013,
abstract = {We prove that any Lattès map can be approximated by strictly postcritically finite rational maps which are not Lattès maps.},
author = {Buff, Xavier, Gauthier, Thomas},
journal = {Bulletin de la Société Mathématique de France},
keywords = {flexible lattès maps; bifurcation measure; hyperbolic sets},
language = {eng},
number = {4},
pages = {603-614},
publisher = {Société mathématique de France},
title = {Perturbations of flexible Lattès maps},
url = {http://eudml.org/doc/272700},
volume = {141},
year = {2013},
}

TY - JOUR
AU - Buff, Xavier
AU - Gauthier, Thomas
TI - Perturbations of flexible Lattès maps
JO - Bulletin de la Société Mathématique de France
PY - 2013
PB - Société mathématique de France
VL - 141
IS - 4
SP - 603
EP - 614
AB - We prove that any Lattès map can be approximated by strictly postcritically finite rational maps which are not Lattès maps.
LA - eng
KW - flexible lattès maps; bifurcation measure; hyperbolic sets
UR - http://eudml.org/doc/272700
ER -

References

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  1. [1] G. Bassanelli & F. Berteloot – « Bifurcation currents in holomorphic dynamics on ℙ k », J. reine angew. Math. 608 (2007), p. 201–235. Zbl1136.37025MR2339474
  2. [2] —, « Lyapunov exponents, bifurcation currents and laminations in bifurcation loci », Math. Ann.345 (2009), p. 1–23. Zbl1179.37067MR2520048
  3. [3] F. Berteloot – « Bifurcation currents in holomorphic families of rational maps », in Pluripotential Theory, Lecture Notes in Math., vol. 2075, Springer, 2013, p. 1–93. Zbl1280.37039MR3089068
  4. [4] X. Buff & A. Epstein – « Bifurcation measure and postcritically finite rational maps », in Complex dynamics, A K Peters, 2009, p. 491–512. Zbl1180.37056MR2508266
  5. [5] L. DeMarco – « Dynamics of rational maps: Lyapunov exponents, bifurcations, and capacity », Math. Ann.326 (2003), p. 43–73. Zbl1032.37029MR1981611
  6. [6] T. Gauthier – « Dimension de Hausdorff de lieux de bifurcations maximales en dynamique des fractions rationnelles », thèse de doctorat, Université Paul Sabatier, 2011, http://tel.archives-ouvertes.fr/tel-00646407. 
  7. [7] —, « Strong bifurcation loci of full Hausdorff dimension », Ann. Sci. Éc. Norm. Supér. 45 (2012), p. 947–984. Zbl1326.37036MR3075109
  8. [8] J. Milnor – « On Lattès maps », in Dynamics on the Riemann sphere, Eur. Math. Soc., Zürich, 2006, p. 9–43. Zbl1235.37015MR2348953
  9. [9] M. Shishikura – « The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets », Ann. of Math.147 (1998), p. 225–267. Zbl0922.58047MR1626737
  10. [10] M. Shishikura & T. Lei – « An alternative proof of Mañé’s theorem on non-expanding Julia sets », in The Mandelbrot set, theme and variations, London Math. Soc. Lecture Note Ser., vol. 274, Cambridge Univ. Press, 2000, p. 265–279. MR1765093

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