Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-12-05T02:08:23.105Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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

[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