International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 251298, 19 pages
doi:10.1155/2008/251298

The attractors of the common differential operator are determined by hyperbolic and lacunary functions

Abstract

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.