International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 251298, 19 pages
Research Article

The Attractors of the Common Differential Operator Are Determined by Hyperbolic and Lacunary Functions

Wolf Bayer

Hans und Hilde Coppi Gymnasium, Römerweg 32, 10318 Berlin, Germany

Received 27 July 2008; Accepted 2 November 2008

Academic Editor: Marco Squassina

Copyright © 2008 Wolf Bayer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For analytic functions, we investigate the limit behavior of the sequence of their derivatives by means of Taylor series, the attractors are characterized by ω-limit sets. We describe four different classes of functions, with empty, finite, countable, and uncountable attractors. The paper reveals that Erdelyiés hyperbolic functions of higher order and lacunary functions play an important role for orderly or chaotic behavior. Examples are given for the sake of confirmation.