Skip to main content Accessibility help
×
Home

The Hausdorff dimension of Julia sets of entire functions

  • Gwyneth M. Stallard (a1)

Abstract

We construct a set of transcendental entire functions such that the Hausdorff dimensions of the Julia sets of these functions have greatest lower bound equal to one.

Copyright

References

Hide All
[1]Baker, I. N.. The domains of normality of an entire function. Ann. Acad. Sci. Fenn. Ser. A I. Math. 1 (1975), 277283.
[2]Brolin, H.. Invariant sets under iteration of rational functions. Arkiv Mat. 6 (1965), 103144.
[3]Duren, P. L.. Univalent Functions. Springer, New York, 1953.
[4]Fatou, P.. Sur les équations fonctionelles. Bull. Soc. Math. France 47 (1919), 161271;
Fatou, P.. Sur les équations fonctionelles. Bull. Soc. Math. France 48 (1920), 3394208314.
[5]Fatou, P.. Sur l'itération des fonctions transcendantes entières. Acta Math. 47 (1926), 337370.
[6]Garber, V.. On the iteration of rational functions. Math. Proc. Camb. Phil. Soc. 84 (1978), 497505.
[7]Hayman, W. K. & Kennedy, P. B.. Subharmonic Functions I. Academic Press, London, 1976.
[8]McMullen, C.. Area and Hausdorff dimension of Julia sets of entire functions. Trans. Amer. Math. Soc. 300 (1987), 329342.
[9]Pólya, G. & Szegö, G.. Problems and Theorems in Analysis I (Part III, problems 158–160). Springer, New York, 1972.
[10]Ruelle, D.. Repellers for real analytic maps. Ergod. Th. & Dynam. Sys. 2 (1982), 99107.

The Hausdorff dimension of Julia sets of entire functions

  • Gwyneth M. Stallard (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed