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

摘要

For analytic functions, we investigate the limit behavior of the sequenceof their derivatives by means of Taylor series, the attractors arecharacterized byω-limit sets. We describe four different classes of functions,with empty, finite, countable, and uncountable attractors. The paper reveals that Erdelyiéshyperbolic functions of higher orderandlacunary functionsplay an important role for orderly or chaotic behavior. Examples are given for the sake of confirmation.