RÝŽOVÁ, Veronika. Birkhoff centre and backward limit points. Topology and its Applications. Amsterdam: Elsevier B.V., 2023, vol. 324, february, p. "108338-1"-"108338-7", 7 pp. ISSN 0166-8641. Available from: https://dx.doi.org/10.1016/j.topol.2022.108338. |
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@article{78284, author = {Rýžová, Veronika}, article_location = {Amsterdam}, article_number = {february}, doi = {http://dx.doi.org/10.1016/j.topol.2022.108338}, keywords = {Backward limit points; Birkhoff centre; Dynamical systems; Recurrent points; s alpha-limit sets; beta-limit sets; omega-limit points}, language = {eng}, issn = {0166-8641}, journal = {Topology and its Applications}, title = {Birkhoff centre and backward limit points}, url = {https://www.sciencedirect.com/science/article/pii/S0166864122003406}, volume = {324}, year = {2023} }
TY - JOUR ID - 78284 AU - Rýžová, Veronika PY - 2023 TI - Birkhoff centre and backward limit points JF - Topology and its Applications VL - 324 IS - february SP - "108338-1"-"108338-7" EP - "108338-1"-"108338-7" PB - Elsevier B.V. SN - 01668641 KW - Backward limit points KW - Birkhoff centre KW - Dynamical systems KW - Recurrent points KW - s alpha-limit sets KW - beta-limit sets KW - omega-limit points UR - https://www.sciencedirect.com/science/article/pii/S0166864122003406 N2 - We suggest one complete and one partial solution to the selected problems presented in the recently published article On Backward Attractors of Interval Maps(Hantakova and Roth (2021) [15]). Specifically we prove a conjecture proposing a characterisation of sets of ss-limit points (i.e. limit points of all accumulation points of backward orbit branches of a specific point) for graph maps. We show that ss-limit sets coincide with Birkhoff centre <(Rec(f))over bar> and that the condition for a point to belong to its ss-limit set is equivalent to belonging to the ss-limit set of an other point. In the second part of the paper we deal with genericity of having all s alpha-limit sets closed and we prove that maps with not all s alpha-limit sets closed are dense in C-0([0,1]), which partially solves an open problem also suggested in the aforementioned article. ER -
RÝŽOVÁ, Veronika. Birkhoff centre and backward limit points. \textit{Topology and its Applications}. Amsterdam: Elsevier B.V., 2023, vol.~324, february, p.~''108338-1''-''108338-7'', 7 pp. ISSN~0166-8641. Available from: https://dx.doi.org/10.1016/j.topol.2022.108338.
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