Area and Hausdorff dimension of the set of accessible points of the Julia sets of λe^z and λ sin(z)

Bogusława Karpińska

Fundamenta Mathematicae (1999)

  • Volume: 159, Issue: 3, page 269-287
  • ISSN: 0016-2736

How to cite

top

Karpińska, Bogusława. "Area and Hausdorff dimension of the set of accessible points of the Julia sets of λe^z and λ sin(z)." Fundamenta Mathematicae 159.3 (1999): 269-287. <http://eudml.org/doc/212334>.

@article{Karpińska1999,
abstract = {},
author = {Karpińska, Bogusława},
journal = {Fundamenta Mathematicae},
keywords = {positive Lebesgue measure; attractor; fixed points; repellor; basin of attraction; Julia set; accessible points; Hausdorff dimension},
language = {eng},
number = {3},
pages = {269-287},
title = {Area and Hausdorff dimension of the set of accessible points of the Julia sets of λe^z and λ sin(z)},
url = {http://eudml.org/doc/212334},
volume = {159},
year = {1999},
}

TY - JOUR
AU - Karpińska, Bogusława
TI - Area and Hausdorff dimension of the set of accessible points of the Julia sets of λe^z and λ sin(z)
JO - Fundamenta Mathematicae
PY - 1999
VL - 159
IS - 3
SP - 269
EP - 287
AB -
LA - eng
KW - positive Lebesgue measure; attractor; fixed points; repellor; basin of attraction; Julia set; accessible points; Hausdorff dimension
UR - http://eudml.org/doc/212334
ER -

References

top
  1. [1] I. N. Baker, Fixpoints and iterates of entire functions, Math. Z. 71 (1959), 146-153. Zbl0168.04002
  2. [2] R. Bowen, Hausdorff dimension of quasi-circles, Inst. Hautes Études Sci. Publ. Math. 50 (1979), 11-26. 
  3. [3] R. L. Devaney and L. Goldberg, Uniformization of attracting basins for exponential maps, Duke Math. J. 2 (1987), 253-266. Zbl0621.30024
  4. [4] R. Devaney and M. Krych, Dynamics of exp(z), Ergodic Theory Dynam. Systems 4 (1984), 35-52. Zbl0567.58025
  5. [5] R. L. Devaney and F. Tangerman, Dynamics of entire functions near the essential singularity, ibid. 6 (1986), 489-503. Zbl0612.58020
  6. [6] P. L. Duren, Univalent Functions, Springer, New York, 1983. 
  7. [7] A. E. Eremenko and M. Yu. Lyubich, Dynamical properties of some classes of entire functions, Ann. Inst. Fourier (Grenoble) 42 (1992), 989-1020. Zbl0735.58031
  8. [8] N. Makarov, On the distortion of boundary sets under conformal mappings, Proc. London Math. Soc. 51 (1985), 369-384. Zbl0573.30029
  9. [9] J. Mayer, An explosion point for the set of endpoints of the Julia set of λexp(z), Ergodic Theory Dynam. Systems 10 (1990), 177-183. 
  10. [10] C. McMullen, Area and Hausdorff dimension of Julia sets of entire functions, Trans. Amer. Math. Soc. 300 (1987), 329-342. Zbl0618.30027
  11. [11] F. Przytycki and M. Urbański, Conformal repellers and ergodic theory, in preparation. Zbl1202.37001
  12. [12] D. Ruelle, Repellers for real analytic maps, Ergodic Theory Dynam. Systems 2 (1982), 99-107. Zbl0506.58024

NotesEmbed ?

top

You must be logged in to post comments.