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

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

Author(s) -

Wolf Bayer

Publication year - 2008

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2008/251298

Subject(s) - lacunary function , mathematics , uncountable set , attractor , countable set , limit (mathematics) , pure mathematics , limit set , hyperbolic function , sequence (biology) , operator (biology) , chaotic , mathematical analysis , biochemistry , chemistry , repressor , artificial intelligence , biology , gene , computer science , genetics , transcription factor

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

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