Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-05T04:18:36.327Z Has data issue: false hasContentIssue false
  • English
  • Français

Meromorphic multifunctions and stability of Julia sets

Published online by Cambridge University Press:  14 October 2010

Shengjian Wu
Shengjian Wu
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, Peoples Republic of China
Get access Rights & Permissions [Opens in a new window]

Abstract

Let Rw(z): W × C∞ → C∞ be an analytic family of rational functions, J(w) the Julia set of Rw and J*(w) the upper semicontinuous regularization of J(w). We shall discuss the relationship between J(w) and J*(w) as well as some related problems.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 6 , December 1995 , pp. 1231 - 1238
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[A]Aupetit, B.. A Primer on Spectral Theory, Springer Verlag, New York, 1991.CrossRefGoogle Scholar
[B]Beardon, A. F.. Iteration of Rational Functions. Springer Verlag, New York, 1991.CrossRefGoogle Scholar
[BH]Branner, A. and Hubbard, J.. The iteration of cubic polynomials, part I: The global topology of parameter space. Ada Math. 160 (1988), 143–206.Google Scholar
[BI]Blanchard, P.. Complex analytic dynamics on the Riemann sphere. Bull. Amer. Math. Soc. 11 (1984), 85–141.CrossRefGoogle Scholar
[BR]Baribeau, L. and Ransford, T. J.. Meromorphic multifunctions and complex dynamics. Ergod. Th. & Dynam. Sys. 12 (1992), 39–52.CrossRefGoogle Scholar
[K]Kriete, H.. The stability of Julia sets. Math. Gottingensis 22 (1988), 1–16.Google Scholar
[L]Lyubich, M.. The dynamics of rational transforms: the topological picture, Russian Math. Surveys 41 (4) (1986), 43–117.CrossRefGoogle Scholar
[MSS]Mane, R., Sad, P. and Sullivan, D.. On the dynamics of rational maps. Ann. Ec. Norm. Sup. 4 (16) (1983), 193–217.CrossRefGoogle Scholar
[S]Sullivan, D.. Quasiconformal homeomorphism and dynamics. I. Ann. Math. (1985), 401–418; III (Preprint).CrossRefGoogle Scholar
[T]Tan, L.. Similarity between the Mandelbrot set and Julia set. Commun. Math. Phys. 134 (1990), 587–617.Google Scholar
[Z]Zalcman, L.. A heuristic principle in complex function theory. Amer. Math. Monthly 85 (1972), 813–817.Google Scholar