Birkhoff centre and backward limit points

@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.