Dynamics of entire functions near the essential singularity
Authors:
- Robert L. DevaneyRDRobert L. Devaney
- Folkert TangermanFTFolkert Tangerman
- 1 December 1986
- journal article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 6 (4) , 489-503
Abstract
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).Keywords
This publication has 15 references indexed in Scilit:
- Area and Hausdorff Dimension of Julia Sets of Entire FunctionsTransactions of the American Mathematical Society, 1987
- Area and Hausdorff dimension of Julia sets of entire functionsTransactions of the American Mathematical Society, 1987
- Structural Instability of exp(z)Proceedings of the American Mathematical Society, 1985
- Bursts into chaosPhysics Letters A, 1984
- Dynamics of exp (z)Ergodic Theory and Dynamical Systems, 1984
- Julia sets and bifurcation diagrams for exponential mapsBulletin of the American Mathematical Society, 1984
- Complex analytic dynamics on the Riemann sphereBulletin of the American Mathematical Society, 1984
- On iterates of ezErgodic Theory and Dynamical Systems, 1981
- An entire function which has wandering domainsJournal of the Australian Mathematical Society, 1976
- Repulsive fixpoints of entire functionsMathematische Zeitschrift, 1968