Birkhoff centre and backward limit points

We suggest one complete and one partial solution to the selected problems presented in the recently published article On Backward Attractors of Interval Maps (Hantáková and Roth (2021) [15]). Specifically we prove a conjecture proposing a characterisation of sets of β-limit points (i.e. limit points...

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Vydáno v:	Topology and its applications Ročník 324; s. 108338
Hlavní autor:	Rýžová, Veronika
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier B.V 01.02.2023
Témata:	Backward limit points Birkhoff centre Dynamical systems Recurrent points sα-limit sets β-limit sets ω-limit points Backward limit points 37B20 ω-limit points 37E25 sα-limit sets Recurrent points Dynamical systems Birkhoff centre 37E05 26A18 β-limit sets
ISSN:	0166-8641, 1879-3207
On-line přístup:	Získat plný text
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Popis
Shrnutí:	We suggest one complete and one partial solution to the selected problems presented in the recently published article On Backward Attractors of Interval Maps (Hantáková and Roth (2021) [15]). Specifically we prove a conjecture proposing a characterisation of sets of β-limit points (i.e. limit points of all accumulation points of backward orbit branches of a specific point) for graph maps. We show that β-limit sets coincide with Birkhoff centre Rec(f)‾ and that the condition for a point to belong to its β-limit set is equivalent to belonging to the β-limit set of an other point. In the second part of the paper we deal with genericity of having all sα-limit sets closed and we prove that maps with not all sα-limit sets closed are dense in C0([0,1]), which partially solves an open problem also suggested in the aforementioned article.
ISSN:	0166-8641 1879-3207
DOI:	10.1016/j.topol.2022.108338