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Connectedness of the tricorn

Published online by Cambridge University Press:  19 September 2008

Shizuo Nakane
Shizuo Nakane
Affiliation:
Tokyo Institute of Polytechnics, 1583 Iiyama, Atsugi, Kanagawa 243-02, Japan
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Abstract

In this note, we show the connectedness of the tricorn, the connectedness locus for the family of antiquadratic maps: fc(z) = + c, c ∈ C.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 2 , June 1993 , pp. 349 - 356
Copyright
Copyright © Cambridge University Press 1993

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References

REFERENCES

[1]Ahlfors, L.. Lectures on Quasiconformal Mappings. Van Nostrand: New York, 1966.Google Scholar
[2]Crowe, W., Hasson, R., Rippon, P. & Strain-Clark, P. E. D.. On the structure of the Mandelbar set. Nonlinearity 2 (1989), 541–553.CrossRefGoogle Scholar
[3]Douady, A.. Systèmes dynamiques holomorphes. uAstérisque 105–106 (1983), 39–63.Google Scholar
[4]Douady, A. & Hubbard, J.. Étude dynamique des polynômes complexes, parts I and II. Publ. Math. d'Orsay (1984–1985).Google Scholar
[5]Douady, A. & Hubbard, J.. Iteration des polynômes quadratiques complexes. C. R. Acad. Sci. Paris, Série I 294 (1982), 123–126.Google Scholar
[6]Lavaurs, P.. Systèmes dynamiques holomorphes: explosion de points périodiques paraboliques. Thesis. Orsay, (1989).Google Scholar
[7]Milnor, J.. Remarks on iterated cubic maps. Exp. Math. 1 (1992), 5–24.Google Scholar
[8]Milnor, J.. Hyperbolic components in spaces of polynomial maps (with an appendix by A. Poirier). Preprint.Google Scholar
[9]Winters, R.. Bifurcations in families of antiholomorphic and biquadratic maps. Thesis at Boston University.Google Scholar