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.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.