Monotonicity of Topological Entropy for One-Parameter Families of Unimodal Mappings
For a special class of one-parameter families of unimodal mappings of the form f t(x): [0, 1] → [0, 1], f t = atx/(x + t), 0 ≤ x ≤ 1/2, we establish that, for t ε [0, 1/(a − 2)], a > 2, the topological entropy h(f t) is a function monotonically increasing in the parameter. We prove that there...
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| Date: | 2003 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2003
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4014 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510143047794688 |
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| author | Volkova, O. Yu. Волкова, О. Ю. Волкова, О. Ю. |
| author_facet | Volkova, O. Yu. Волкова, О. Ю. Волкова, О. Ю. |
| author_sort | Volkova, O. Yu. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:18:28Z |
| description | For a special class of one-parameter families of unimodal mappings of the form f t(x): [0, 1] → [0, 1], f t = atx/(x + t), 0 ≤ x ≤ 1/2, we establish that, for t ε [0, 1/(a − 2)], a > 2, the topological entropy h(f t) is a function monotonically increasing in the parameter. We prove that there exists a class of one-parameter families of unimodal mappings f t that contains the family indicated above and establish conditions under which the topological entropy h(f t) is a function monotonically increasing in the parameter. |
| first_indexed | 2026-03-24T02:52:18Z |
| format | Article |
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| id | umjimathkievua-article-4014 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:52:18Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/85/8e71ef577693620ea201c3846fec4285.pdf |
| spelling | umjimathkievua-article-40142020-03-18T20:18:28Z Monotonicity of Topological Entropy for One-Parameter Families of Unimodal Mappings Монотонность топологической энтропии для одпопараметрических семейств унимодальных отображений Volkova, O. Yu. Волкова, О. Ю. Волкова, О. Ю. For a special class of one-parameter families of unimodal mappings of the form f t(x): [0, 1] → [0, 1], f t = atx/(x + t), 0 ≤ x ≤ 1/2, we establish that, for t ε [0, 1/(a − 2)], a > 2, the topological entropy h(f t) is a function monotonically increasing in the parameter. We prove that there exists a class of one-parameter families of unimodal mappings f t that contains the family indicated above and establish conditions under which the topological entropy h(f t) is a function monotonically increasing in the parameter. Для деякого спеціального, класу одпопараметричпих сімей уиімодальних відображень $f_t(x): [0, 1] → [0, 1], f_t = atx/(x + t),\; 0 ≤ x ≤ 1/2,$, для $t ε [0, 1/(a − 2)], a > 2,$ було встановлено, що топологічна ентропія $h(f_t)$ — монотонно зростаюча за параметром функція. У цій роботі доведено, що існує деякий клас одпопараметричпих сімей уиімодальних відображень $f_t$ до якого належить наведена вище сім'я, а також встановлено умови, при яких топологічна ентропія $h(f_t)$— монотонно зростаюча за параметром функція. Institute of Mathematics, NAS of Ukraine 2003-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4014 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 11 (2003); 1443-1449 Український математичний журнал; Том 55 № 11 (2003); 1443-1449 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4014/4739 https://umj.imath.kiev.ua/index.php/umj/article/view/4014/4740 Copyright (c) 2003 Volkova O. Yu. |
| spellingShingle | Volkova, O. Yu. Волкова, О. Ю. Волкова, О. Ю. Monotonicity of Topological Entropy for One-Parameter Families of Unimodal Mappings |
| title | Monotonicity of Topological Entropy for One-Parameter Families of Unimodal Mappings |
| title_alt | Монотонность топологической энтропии для одпопараметрических
семейств унимодальных отображений |
| title_full | Monotonicity of Topological Entropy for One-Parameter Families of Unimodal Mappings |
| title_fullStr | Monotonicity of Topological Entropy for One-Parameter Families of Unimodal Mappings |
| title_full_unstemmed | Monotonicity of Topological Entropy for One-Parameter Families of Unimodal Mappings |
| title_short | Monotonicity of Topological Entropy for One-Parameter Families of Unimodal Mappings |
| title_sort | monotonicity of topological entropy for one-parameter families of unimodal mappings |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4014 |
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