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Dynamics of exp (z)

Published online by Cambridge University Press:  19 September 2008

Robert L. Devaney  and
Michal Krych
Robert L. Devaney
Affiliation:
Department of Mathematics, Boston University, Boston, Mass. 02215, USA
Michal Krych
Affiliation:
Department of Mathematics, Tufts University, Medford, Mass. 02155, USA
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Abstract

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We describe the dynamical behaviour of the entire transcendental function exp(z). We use symbolic dynamics to describe the complicated orbit structure of this map whose Julia Set is the entire complex plane. Bifurcations occurring in the family c exp(z) are discussed in the final section.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 1 , March 1984 , pp. 35 - 52
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

[1]Brolin, . Invariant sets under iteration of rational functions. Arkiv. für Matematik. 6 (1965) 103–144.CrossRefGoogle Scholar
[2]Douady, A. & Hubbard, J.. Iteration des polynômes quadratiques complexes. C.R. Acad. Sci. Paris 294 18 01, 1982.Google Scholar
[3]Fatou, P.. Sur l'iteration des fonctions transcendantes entieres. Acta Math. 47 (1926), 337–370.CrossRefGoogle Scholar
[4]Julia, G.. Iteration des applications fonctionnelles. J. Math. Pures Appl. (1918), 47–245.Google Scholar
[5]Mandelbrot, B.. The Fractal Geometry of Nature. Freeman, 1982.Google Scholar
[6]Mañé, R., Sad, P. & Sullivan, D.. On the dynamics of rational maps. To appear.Google Scholar
[7]Misiurewicz, M.. On iterates of ez. Ergod. Th. & Dynam. Sys. 1 (1981), 103–106.CrossRefGoogle Scholar
[8]Sullivan, D.. Conformal dynamical systems. To appear.Google Scholar
[9]Sullivan, D.. Quasi-conformal homeomorphisms and dynamics III. To appear.Google Scholar