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Bifurcation to an entire function

Published online by Cambridge University Press:  20 June 2003

R. R. BHATTACHARJEE
R. R. BHATTACHARJEE
Affiliation:
Department of Mathematics, Boston University, Boston, MA 02215, USA (e-mail: [email protected])
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Abstract

In this paper we will consider a bifurcation that occurs in the topology of the Julia set of meromorphic maps as they become entire. For some meromorphic maps the Julia set will be a Cantor set. We will investigate how the Julia set changes as these meromorphic maps approach the entire function whose Julia set is a Cantor bouquet. Other meromorphic maps have a Julia set that is a Jordan curve. Again we will study how this curve changes as these meromorphic maps approach the entire function whose Julia set is a Cantor bouquet.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 3 , June 2003 , pp. 693 - 705
Copyright
2003 Cambridge University Press

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