Topological Limit of Trajectories of Intervals of Simplest One-Dimensional Dynamical Systems
We consider dynamical systems generated by continuous maps of an interval into itself. We investigate the asymptotic behavior of the trajectories of subsets of the interval. In particular, we prove that if the ω-limit set of an arbitrary trajectory is a fixed point, then the topological limit of the...
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| Date: | 2002 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2002
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4080 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510213148246016 |
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| author | Fedorenko, V. V. Федоренко, В. В. Федоренко, В. В. |
| author_facet | Fedorenko, V. V. Федоренко, В. В. Федоренко, В. В. |
| author_sort | Fedorenko, V. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:20:31Z |
| description | We consider dynamical systems generated by continuous maps of an interval into itself. We investigate the asymptotic behavior of the trajectories of subsets of the interval. In particular, we prove that if the ω-limit set of an arbitrary trajectory is a fixed point, then the topological limit of the trajectory of any subinterval exists. |
| first_indexed | 2026-03-24T02:53:25Z |
| format | Article |
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| id | umjimathkievua-article-4080 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:53:25Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/d4/7e3f1db31d6eba749ad43c47ddd51dd4.pdf |
| spelling | umjimathkievua-article-40802020-03-18T20:20:31Z Topological Limit of Trajectories of Intervals of Simplest One-Dimensional Dynamical Systems Топологический предел траекторий интервалов простейших одномерных динамических систем Fedorenko, V. V. Федоренко, В. В. Федоренко, В. В. We consider dynamical systems generated by continuous maps of an interval into itself. We investigate the asymptotic behavior of the trajectories of subsets of the interval. In particular, we prove that if the ω-limit set of an arbitrary trajectory is a fixed point, then the topological limit of the trajectory of any subinterval exists. Розглядаються динамічні системи, породжені неперервними відображеннями інтервалу в себе. Досліджується асимптотична поведінка траєкторій підмножин інтервалу. Зокрема доведено, що якщо ω-гранична множина довільної траєкторії — нерухома точка, то топологічна границя траєкторії будь-якого підінтервалу існує. Institute of Mathematics, NAS of Ukraine 2002-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4080 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 3 (2002); 425-430 Український математичний журнал; Том 54 № 3 (2002); 425-430 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4080/4870 https://umj.imath.kiev.ua/index.php/umj/article/view/4080/4871 Copyright (c) 2002 Fedorenko V. V. |
| spellingShingle | Fedorenko, V. V. Федоренко, В. В. Федоренко, В. В. Topological Limit of Trajectories of Intervals of Simplest One-Dimensional Dynamical Systems |
| title | Topological Limit of Trajectories of Intervals of Simplest One-Dimensional Dynamical Systems |
| title_alt | Топологический предел траекторий интервалов простейших одномерных динамических систем |
| title_full | Topological Limit of Trajectories of Intervals of Simplest One-Dimensional Dynamical Systems |
| title_fullStr | Topological Limit of Trajectories of Intervals of Simplest One-Dimensional Dynamical Systems |
| title_full_unstemmed | Topological Limit of Trajectories of Intervals of Simplest One-Dimensional Dynamical Systems |
| title_short | Topological Limit of Trajectories of Intervals of Simplest One-Dimensional Dynamical Systems |
| title_sort | topological limit of trajectories of intervals of simplest one-dimensional dynamical systems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4080 |
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