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Dynamics of entire functions near the essential singularity

Published online by Cambridge University Press:  19 September 2008

Robert L. Devaney  and
Folkert Tangerman
Robert L. Devaney
Affiliation:
Department of Mathematics, Boston University, Boston, Mass. 02215, USA
Folkert Tangerman
Affiliation:
Department of Mathematics, Boston University, Boston, Mass. 02215, USA
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Abstract

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We show that entire functions which are critically finite and which meet certain growth conditions admit ‘Cantor bouquets’ in their Julia sets. These are invariant subsets of the Julia set which are homeomorphic to the product of a Cantor set and the line [0, ∞). All of the curves in the bouquet tend to ∞ in the same direction, and the map behaves like the shift automorphism on the Cantor set. Hence the dynamics near ∞ for these types of maps may be analyzed completely. Among the entire maps to which our methods apply are exp (z), sin (z), and cos (z).

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 4 , December 1986 , pp. 489 - 503
Copyright
Copyright © Cambridge University Press 1986

References

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