The Attractors of the Common Differential Operator Are Determined by Hyperbolic and Lacunary Functions
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 th...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/251298 |
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| _version_ | 1832559944274018304 |
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| author | Wolf Bayer |
| author_facet | Wolf Bayer |
| author_sort | Wolf Bayer |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-fbe7799831944687996de45401daaa88 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fbe7799831944687996de45401daaa882025-02-03T01:28:57ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/251298251298The Attractors of the Common Differential Operator Are Determined by Hyperbolic and Lacunary FunctionsWolf Bayer0Hans und Hilde Coppi Gymnasium, Römerweg 32, 10318 Berlin, GermanyFor 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.http://dx.doi.org/10.1155/2008/251298 |
| spellingShingle | Wolf Bayer The Attractors of the Common Differential Operator Are Determined by Hyperbolic and Lacunary Functions International Journal of Mathematics and Mathematical Sciences |
| title | The Attractors of the Common Differential Operator Are Determined by Hyperbolic and Lacunary Functions |
| title_full | The Attractors of the Common Differential Operator Are Determined by Hyperbolic and Lacunary Functions |
| title_fullStr | The Attractors of the Common Differential Operator Are Determined by Hyperbolic and Lacunary Functions |
| title_full_unstemmed | The Attractors of the Common Differential Operator Are Determined by Hyperbolic and Lacunary Functions |
| title_short | The Attractors of the Common Differential Operator Are Determined by Hyperbolic and Lacunary Functions |
| title_sort | attractors of the common differential operator are determined by hyperbolic and lacunary functions |
| url | http://dx.doi.org/10.1155/2008/251298 |
| work_keys_str_mv | AT wolfbayer theattractorsofthecommondifferentialoperatoraredeterminedbyhyperbolicandlacunaryfunctions AT wolfbayer attractorsofthecommondifferentialoperatoraredeterminedbyhyperbolicandlacunaryfunctions |