On negative limit sets for one-dimensional dynamics |
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| Authors: | Francisco BalibreaMarek Lampart Piotr Oprocha |
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| Institution: | a Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spainb Mathematical Institute of the Silesian University in Opava, Silesian University of Opava, Na Rybní?ku 1, 746 01 Opava, Czech Republicc Department of Applied Mathematics and IT4 Innovations, VŠB - Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava, Czech Republicd AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Kraków, Polande Institute of Mathematics, Polish Academy of Sciences, ul. ?niadeckich 8, 00-956 Warszawa, Poland |
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| Abstract: | In this paper we study the structure of negative limit sets of maps on the unit interval. We prove that every α-limit set is an ω-limit set, while the converse is not true in general. Surprisingly, it may happen that the space of all α-limit sets of interval maps is not closed in the Hausdorff metric (and thus some ω-limit sets are never obtained as α-limit sets). Moreover, we prove that the set of all recurrent points is closed if and only if the space of all α-limit sets is closed. |
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| Keywords: | primary 37E05 secondary 37B20 37B40 |
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