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 sequence of their derivatives bymeans of Taylor series, the attractors are characterized by ω-limit sets. We describe four differentclasses of functions, with empty, finite, countable, and uncountable attractors. The paper revealsthat Erdelyies hyperbolic functions of higher order and lacunary functions play an important role fororderly or chaotic behavior. Examples are given for the sake of confirmation.