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...

Full description

Saved in:
Bibliographic Details
Published in:Topology and its applications Vol. 324; p. 108338
Main Author: Rýžová, Veronika
Format: Journal Article
Language:English
Published: Elsevier B.V 01.02.2023
Subjects:
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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