J
2023
Birkhoff centre and backward limit points
RÝŽOVÁ, Veronika
Basic information
Original name
Birkhoff centre and backward limit points
Authors
RÝŽOVÁ, Veronika (203 Czech Republic, guarantor, belonging to the institution)
Edition
Topology and its Applications, Amsterdam, Elsevier B.V. 2023, 0166-8641
Other information
Type of outcome
Článek v odborném periodiku
Field of Study
10101 Pure mathematics
Country of publisher
Netherlands
Confidentiality degree
není předmětem státního či obchodního tajemství
RIV identification code
RIV/47813059:19610/23:A0000143
Organization unit
Mathematical Institute in Opava
Keywords in English
Backward limit points; Birkhoff centre; Dynamical systems; Recurrent points; s alpha-limit sets; beta-limit sets; omega-limit points
Tags
International impact, Reviewed
V originále
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.
Displayed: 25/11/2024 14:24